Very important. This is evident in the Bible itself from God's perspective and not man's. Let me explain.
God is very strong in the scriptures about his honesty and trustworthiness. Even if God would rather not do something, He has to do it if He previously said He would for the sake of His Good Name. Because of His Good Name and Character, God cannot and will not go back on anything He has said, ever!
With this in mind, I refer you to the prophecies from God through out the Bible from Genesis to Revelation. These prophecies seek to show humans the power and foresight and truth of God. They help humans to see that God is who He is.
If we look at people like Nostradamus and Baba Vanga, they do not prophecy the words of the Holy Spirit. Their sources of prophecy are from non-Godly sources. This is evident in that not all of their prophecies are true. Yet, all of God's prophecies do come true as our expert witness, world history, testifies to.
For example, the ancient Hebrew version of the geneology in Genesis 5 provides this prophecy:
Man given mortal sorrow. The Blessed God shall come down, discipling. His death shall bring the despairing comfort, rest.
ADAM = MAN
SETH = APPOINTED, GRANTED, GIVEN
ENOSH = MORTAL, FRAIL, FEEBLE
KENAN = SORROW, DIRGE, LAMENTATION
MAHALALEL = THE BLESSED GOD, THE PRAISEWORTHY GOD
JARED = SHALL COME DOWN
ENOCH = DISCIPLING
METHUSELAH = HIS DEATH SHALL BRING
LAMECH = THE DESPAIRING
NOAH = COMFORT, REST
So, we can see that God has given us foresight through this geneology, that a feeble man of mortal frame will come who is greatly afflicted and of God that will die, and that his death will bring the suffering comfort and rest.
In Isaiah 9:6, again we see that a human will be born to us. But this time it is more explicit, and states that this man is God our Father, the Holy Spirit who will come in human form:
For to us a child is born,
to us a son is given,
and the government will be on his shoulders.
And he will be called
Wonderful Counselor, Mighty God,
Everlasting Father, Prince of Peace.
So, in Isaiah 9:6, God has validated who the person of Genesis 5 will be. Further validation that Isaiah 9:6 is speaking about the same person is mentioned in Isaiah 53:
53 Who has believed our message
and to whom has the arm of the Lord been revealed?
2 He grew up before him like a tender shoot,
and like a root out of dry ground.
He had no beauty or majesty to attract us to him,
nothing in his appearance that we should desire him.
3 He was despised and rejected by mankind,
a man of suffering, and familiar with pain.
Like one from whom people hide their faces
he was despised, and we held him in low esteem.
4 Surely he took up our pain
and bore our suffering,
yet we considered him punished by God,
stricken by him, and afflicted.
5 But he was pierced for our transgressions,
he was crushed for our iniquities;
the punishment that brought us peace was on him,
and by his wounds we are healed.
6 We all, like sheep, have gone astray,
each of us has turned to our own way;
and the Lord has laid on him
the iniquity of us all.
7 He was oppressed and afflicted,
yet he did not open his mouth;
he was led like a lamb to the slaughter,
and as a sheep before its shearers is silent,
so he did not open his mouth.
8 By oppression[a] and judgment he was taken away.
Yet who of his generation protested?
For he was cut off from the land of the living;
for the transgression of my people he was punished.[b]
9 He was assigned a grave with the wicked,
and with the rich in his death,
though he had done no violence,
nor was any deceit in his mouth.
10 Yet it was the Lord’s will to crush him and cause him to suffer,
and though the Lord makes[c] his life an offering for sin,
he will see his offspring and prolong his days,
and the will of the Lord will prosper in his hand.
11 After he has suffered,
he will see the light of life[d] and be satisfied[e];
by his knowledge[f] my righteous servant will justify many,
and he will bear their iniquities.
12 Therefore I will give him a portion among the great,[g]
and he will divide the spoils with the strong,[h]
because he poured out his life unto death,
and was numbered with the transgressors.
For he bore the sin of many,
and made intercession for the transgressors.
Now, bear in mind that it is God who is the author and originator of our Christian Faith. And God validates what He says and shows throughout the scripture. He does so, so that generation afer generation can know they can trust His Holy Written Word.
God further validates this person of Genesis 5, Isaiah 9:6, and Isaiah 53 in Zechariah 9:9. We read:
The Coming of Zion’s King
9 Rejoice greatly, Daughter Zion!
Shout, Daughter Jerusalem!
See, your king comes to you,
righteous and victorious,
lowly and riding on a donkey,
on a colt, the foal of a donkey.
We can acknowledge that this person is the person Jesus of the New Testament, as in Luke 19:28-40, we read:
Jesus Comes to Jerusalem as King
28 After Jesus had said this, he went on ahead, going up to Jerusalem. 29 As he approached Bethphage and Bethany at the hill called the Mount of Olives, he sent two of his disciples, saying to them, 30 “Go to the village ahead of you, and as you enter it, you will find a colt tied there, which no one has ever ridden. Untie it and bring it here. 31 If anyone asks you, ‘Why are you untying it?’ say, ‘The Lord needs it.’”
32 Those who were sent ahead went and found it just as he had told them. 33 As they were untying the colt, its owners asked them, “Why are you untying the colt?”
34 They replied, “The Lord needs it.”
35 They brought it to Jesus, threw their cloaks on the colt and put Jesus on it. 36 As he went along, people spread their cloaks on the road.
37 When he came near the place where the road goes down the Mount of Olives, the whole crowd of disciples began joyfully to praise God in loud voices for all the miracles they had seen:
38 “Blessed is the king who comes in the name of the Lord!”[a]
“Peace in heaven and glory in the highest!”
39 Some of the Pharisees in the crowd said to Jesus, “Teacher, rebuke your disciples!”
40 “I tell you,” he replied, “if they keep quiet, the stones will cry out.”
I could continue this narrative of God's historical verification of events by His prophecying the years in advance, and having people write them down when they happen for future generations like ours to read, validate, and accept.
The people of Luke's time had the Old Testament prophecies to identify the coming Messiah. Today, we have the New Testament that testifies to and verifies the Old Testament narrative. We have the Old Testament that testifies to and verifies the New Testament. And we have the many wonderful examples of God's loving kindness towards the sinful human race in the many testimonies of people who have been converted, exorcised (delivered), and healed even to the present day.
Two very good examples of historical Bible event verification that led to the conversion of two very staunch athiests are James Warner Wallace, author of Cold Case Christianity and Lee Strobel the author of The Case for Christ. Both these people became Christians on the weight of evidence that verifies the truth and validity and historical accuracy of the Old and New Testament writings upon which we as Christians base our faith.
And so our faith in God and the scriptures is not a blind faith but an evidencial one that has been time and battle tested to stand the tests of time. And we as Christians can walk confidently in the knowledge that accepting the free gift of salvation through Jesus Christ and repenting of our sins will lead us to eternal life with God our Eternal and loving Father.
Peace be with you.