I am hoping to understand or know if Jesus' apostles would have had gathering relics of something like the crucifixion in mind at some point when it as still possible to locate them (ex: the true cross, crown of thorns, nails), such as a few days following the crucifixion?
Was this something Jews had a habit of doing for Holy men during Christ's time on earth? Unless this was a cultural/religious practice, I have some skepticism on the likelihood that this would have been a priority.
Neither Britannica nor Wikipedia list any form of relics within Judaism.
Collecting relics was effectively never done by the Israelites or Jews. To them, only God (and God through his agents) has supernatural power. Believing that relics or other objects have supernatural power, in principle, violates the first and second commandments, "Thou shalt have no other gods before me" and "Thou shalt not make unto thee any graven image". It in effect turns the object into a form of god.
Ancient Greeks though, did believe in the power of relics, and this belief passed on to the Roman Empire and the Holy Roman Empire.
It wasn't until the Roman Church became the official Christian form of Christianity that anyone thought to collect Christian relics.
Constantine's mother, Empress Helena, was particularly interested in relics, artefacts, and locations. She herself made a pilgrimage to Palestine and other provinces where she built churches on holy sites, including the location of Moses's burning bush. At the site of Jesus's tomb, she had three crosses excavated and used a miracle to determine which one was the True Cross. She also discovered the crucifixion nails and placed one in Constantine's helmet and one in his horse's bridle. She is also thought to have found Jesus's Holy Tunic.
Helena explicitly sent her men to locate holy relics. Given what failure would have meant, all these missions were of course successful. Other finds included the rope used to tie Jesus to the cross, more pieces of the cross, and more of the Holy Tunic.
Centuries later, many Crusaders returned with "genuine" relics they had liberated from the holy land. Some were naïve dupes, while others were scoundrels in their own right. The number of nails and pieces of the true cross that were brought back would have been sufficient to build a church or two.
In reality, the chance that anyone would have preserved Jesus's cross or its nails, his crown of thorns, his blood, etc. are extremely close to zero.
Was the Gathering Relics of Holy Men in 1st Century common in the Early Church?
The idea of showing respect to the dead the dead is evident in the Scriptures.
In antiquity, we see the Jews taking the body of Joseph out of the Land of Egypt, when they left their oppressors.
Moses took the bones of Joseph with him because Joseph had made the Israelites swear an oath. He had said, "God will surely come to your aid, and then you must carry my bones up with you from this place." (Exodus 13:19)
The ancient Jews also took care to place Jacob within the boundary of Israel.
The bones of Jacob, which the Israelites had brought out from Egypt, they buried at Shechem, in a piece of land that Jacob had bought from the children of Hamor, the father of Shechem, for one hundred pieces of money; it became an inheritance for the descendants of Joseph. And Eleazar son of Aaron died; and they buried him in Gibeah in the hill country of Ephraim, which had been given to his son Phinehas. (Joshua 24:32-33)
We can read about the account of God working a Miracle through the touching of the bones of Elisha in 2 Kings.
Once while some Israelites were burying a man, suddenly they saw a band of raiders; so they threw the man’s body into Elisha’s tomb. When the body touched Elisha’s bones, the man came to life and stood up on his feet. 2 Kings 13:21
It is also known that both Jews and Christians (as well as Muslims) have retained the idea of visiting the relics in some degree or other of many biblical persons in the history of salvation. Wikipedia lists the burial places of biblical figures. I would think that the relics or bones of the saints or martyrs would definitely be gathered for proper burial and remembrance when possible. The Jews even visit the tomb of Adam and Eve in the Cave of the Patriarchs!
We also see in Acts how the followers of Jesus were in a sense creating a sort of third class relic (as we say in the Catholic Church) by applying handkerchiefs and aprons to the Apostle St. Paul and then taking them home to the sick.
When handkerchiefs or aprons that had merely touched his skin were placed on sick people, they were healed of their diseases, and evil spirits were expelled. (Acts 19:12)
There is also the story of the robe that is mentioned in 2 Timothy. Whether it is his personal robe or if it could be Our Lord's robe from his Passion we are not told. Scripture is silent on this issue. In any case it had some value to the Apostle Paul.
Near the end of the Apostle Paul’s life he wrote Timothy, his “son in the faith,” his last inspired epistle. Paul was about to be beheaded for the cause of Christ under the tyranny of the Roman Emperor Nero and, therefore, charged Timothy to “hold fast the pattern of sound words” which he had heard from Paul (2 Tim. 1:13 NKJV). Paul was passing the baton, as it were, to Timothy before the Apostle would go home to be with the Lord. Paul gave several moving exhortations to Timothy in this epistle. Paul called upon Timothy to “be strong in the grace that is in Christ Jesus” (2 Tim. 2:1). Paul desired him to teach “faithful men” (2 Tim. 2:2), and Paul admonished him to “be diligent to present yourself approved to God” (2 Tim. 2:15). After praising Timothy’s faithfulness, Paul wrote, “you must continue in the things which you have learned” (2 Tim. 3:14). Yet, as Paul neared the end of his final letter, he included something that appears trivial, mundane, and out of place. “Bring the cloak that I left with Carpus at Troas when you come – and the books, especially the parchments” (2 Tim. 4:13a). The Apostle Paul, soon to be a martyr, asked his most faithful student
The Apostle Paul, soon to be a martyr, asked his most faithful student, his best hope for the furtherance of the gospel of the grace of God, to bother with a cloak. It is understandable that there were books and parchments important to the Apostle, but a cloak seems irrelevant. No details are given about the nature of this cloak, where it originated, if it was a sentimental gift, or why it would have been special to the imprisoned Apostle in Rome. It would seem that Paul could have found another cloak in Rome to stay warm, but perhaps poverty prevented it. Regardless, under inspiration of the Holy Spirit, the Apostle Paul asked Timothy to locate this cloak and carry it from modern day Turkey all the way to Italy. Since this was Paul’s last epistle, there is no way to know if Timothy was successful in fulfilling the request.
It is natural to wonder why such a seemingly minute detail would be included in the inspired canon of God’s Word. The Holy Spirit saw fit to include the request for the cloak for some reason. Perhaps it was to show believers a glimpse of what life for the saints was like in the years after the crucifixion of Christ. Maybe the cloak is mentioned to illustrate the hardships of the Apostle Paul and the lack of resources he faced at the end of his ministry. These are possibilities. Yet, it seems probable that the cloak was included to demonstrate to believers that the doctrines that Paul charged Timothy to uphold were to be lived out in the mundane everyday details of life. The grace of God that had seized Timothy’s heart would have compelled him to serve his “father in the faith,” and he would have found the cloak, slung it over his shoulder, and carried it hundreds of miles by land and sea. I think Paul’s cloak was included in Scripture to show us how we can live out the grace of God and serve others. This seemingly trivial detail proclaims that there is no part of life that the grace of God does not affect. He works in the everyday things of life. - Paul’s Cloak
If anyone would have gathered relics of Christ and his Passion, certainly the Virgin Mary would have been the first. Not only was she intimately aware of Jesus' divinity, she was also his mother. Although maybe not historically noted, Mel Gibson's movie on the Passion of the Christ demonstrates how Mary could have saved some of Christ's sacred blood after the scourging at the pillar. Here is a small excerpt on it on YouTube: The Passion of the Christ Through Mary's Eyes Mary was fully aware the Christ's blood was holy, sacred and divine.
The idea of bones (relics) having some supernatural power probably sources to the story of the dead man touching the bones of Elisha and returning to life.
And it came to pass, as they were burying a man, that, behold, they spied a band of men; and they cast the man into the sepulchre of Elisha: and when the man was let down, and touched the bones of Elisha, he revived, and stood up on his feet. 2 Ki 13:21
In addition, the due respect of the dead would source back to Joseph's request when the Israelites left Egypt.
And Joseph said unto his brethren, I die: and God will surely visit you, and bring you out of this land unto the land which he sware to Abraham, to Isaac, and to Jacob. And Joseph took an oath of the children of Israel, saying, God will surely visit you, and ye shall carry up my bones from hence. Gen 50:24-25
This great example of faith in God's promises was carried out by Moses and mentioned in the list of faith examples in Hebrews 11.
And Moses took the bones of Joseph with him: for he had straitly sworn the children of Israel, saying, God will surely visit you; and ye shall carry up my bones away hence with you. Exo 13:19
By faith Joseph, when he died, made mention of the departing of the children of Israel; and gave commandment concerning his bones. Heb 11:22
In those examples, it wasn't so much that the bones had some mystical power, but rather they represented the reality of God's promises.
At the time of Christ, they no more would revere bones, than touch them. It was against the Law of Moses.
He that toucheth the dead body of any man shall be unclean seven days. Num 19:11
And Christ will contrast the idea of clean on the outside, while dead on the inside.
Woe unto you, scribes and Pharisees, hypocrites! for ye are like unto whited sepulchres, which indeed appear beautiful outward, but are within full of dead men's bones, and of all uncleanness. Mat 23:27
So to answer the OP, there is no belief in the power of bones at Christ's time and no indication of Christians who were revering inanimate objects.
But subequent to the ascension some hundreds of years later, like with Elisha, there were factions that again saw bones (relics) as somehow useful to "hear" God. The earliest account, not of relic gathering, but of recognizing God's promises, is written in the Martrydom of Polycarp circa 170.
The centurion then, seeing the strife excited by the Jews, placed the body [of Polycarp] in the midst of the fire, and consumed it. Accordingly, we afterwards took up his bones, as being more precious than the most exquisite jewels, and more purified than gold, and deposited them in a fitting place, whither, being gathered together, as opportunity is allowed us, with joy and rejoicing, the Lord shall grant us to celebrate the anniversary of his martyrdom, both in memory of those who have already finished their course, and for the exercising and preparation of those yet to walk in their steps. -source-
As well there is the case of the marytrs of Lyons, such as Blandina.
The heathen were not content with putting the martyrs to death with tortures, or allowing them to die in prison. They cast their dead bodies to the dogs, and caused them to be watched day and night, lest the other Christians should give them burial; and after this, they burnt the bones, and threw the ashes of them into the river Rhone, by way of mocking at the notion of a resurrection. For, as St. Paul had found at Athens (Acts xvii. 32), and elsewhere, there was no part of the Gospel which the heathen in general thought so hard to believe as the doctrine that that which is “sown in corruption” shall hereafter be “raised in incorruption;” that that which “is sown a natural body” will one day be “raised a spiritual body” -source-
The idea of burning a Christian's body so as to leave nothing for God to work with is laughable, but unfortunately some took that attitude too far in the opposite direction that God would work bones or inanimate objects such as thorns, a cup, a piece of wood for the living.
In any event, there's no sense of the idea that came to grow later in the church of some latent power in relics, but rather just a keen awareness of God's promises and faithful people.
