OP: why the disciples were able to accept Christ as Messiah while not undertaking the rigorous check-the-box exercise that they were most likely at least familiar with?
The Gospels are filled with examples of "check the box" and the process from their "all in" acceptance to "all out" rejection and then back to "all in".
The other thing to keep in mind is there are many scriptures besides Zephania to be understood in this process.
One last thing that ties with all of scripture is that the idea of one permanent visitation versus the two that are currently going on is a conundrum for those who are stuck on the sole idea that Messiah was only a conquering King, rather than understanding Messiah as Suffering Servant.
Check the Box
But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, thou son of David, fear not to take unto thee Mary thy wife: for that which is conceived in her is of the Holy Ghost. Mt 1:20 re Isa 7:14
And thou Bethlehem, in the land of Juda, art not the least among the princes of Juda: for out of thee shall come a Governor, that shall rule my people Israel. Mt 2:6 re Mic 5:2
The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, Lk 4:18 re Isa 11:2
I could go on, but their "checking the boxes" led to 3 1/2 years of close attendance to Christ's ministry. The problem was they only thought in terms of Kingship.
Then Simon Peter having a sword drew it, and smote the high priest's servant, and cut off his right ear. The servant's name was Malchus. Jn 18:10
And they said, Lord, behold, here are two swords. And he said unto them, It is enough. Lk 22:38
They were "all in", willing to die for their beliefs. But they were seeing their King, and so He was, but not grasping the Suffering Servant requirement.
And Peter remembered the word of Jesus, which said unto him, Before the cock crow, thou shalt deny me thrice. And he went out, and wept bitterly. Mt 26:75
Then she runneth, and cometh to Simon Peter, and to the other disciple, whom Jesus loved, and saith unto them, They have taken away the Lord out of the sepulchre, and we know not where they have laid him. Then went in also that other disciple, which came first to the sepulchre, and he saw, and believed [that the body was missing]. For as yet they knew not the scripture, that he must rise again from the dead. Jn 20:2, 8-9
They were done. Still concerned, but thought the Messiahship was sunk.
Upon His proving He is the resurrected Servant and King, they were again all in, yet, the idea lingered.
When they therefore were come together, they asked of him, saying, Lord, wilt thou at this time restore again the kingdom to Israel? Acts 1:6
We might surmise that the apostles wondered about the same question as the OP, saying Jesus you fulfilled the Suffering Servant prophecies, although we expected Messiah to fulfill the King prophecies first and perhaps only, but now that You have risen from the dead, is it time for the full fulfillment of all prophecy?
And he said unto them, It is not for you to know the times or the seasons, which the Father hath put in his own power. Acts 1:7
Ok, and they continued all in.
These all continued with one accord in prayer and supplication, with the women, and Mary the mother of Jesus, and with his brethren. Acts 1:14
And when the day of Pentecost was fully come, they were all with one accord in one place. And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance. Acts 2:1, 4
Subsequent to the New Testament record, Christian tradition shows the disciples spreading out from Jerusalem to Samaria to the ends of the earth.
So, to answer the OP, this is the pattern of their thinking from the beginning of Christ's ministry to His ascension to Pentecost and thereafter.