Pretty much. Also, we tend to accept facts like "Julius Caesar was born in Subaru" when our only source is some guy said that 200 years after he was born. So in terms of Historical records, the New Testament is actually pretty contemporary, being written mere decades after Jesus existed. My faith primarily hinges on Jesus' and the New Testament
So ain't that the reason to doubt that Caesar was born in Subaru and seek more evidence, as opposed to believe the New Testament? Also, given the supernatural claims about Jesus, shouldn't it be supplied with extraordinary evidence?
We know for sure that Caesar did exist and was the Roman dictator, for example. We also have contemporary sources on his life - accounts of Cicero, for example, or Sallust.
Can we say for sure that Jesus did exist, and, especially important, has actually created any miracles?
And also, what about evidence for the existence of Buddha, for example? Did he never exist or he never attained nirvana, or he falsely believed he switched to some supernatural state while this was all mental? Or did it all exist in parralel?
There were several sources for Jesus doing miracles - not just the ones contained in the New Testament, but Celsus as well as the Talmud affirmed the miracles, but just put them down as sorcery.
What sort of extraordinary evidence are you looking for, exactly? Jesus didn't lead an army or a nation so you'd be hard pressed to find coins with His face on them. He did leave a Church though which there is evidence from, and that it just spawned at a specific period of time. So something clearly happened
As for Buddha, Buddha is dead. Buddha didn't even claim to be a god or a prophet. Buddhism appears to be more of a philosophy than a theistic religion.
Both of the sources you listed come from way after the beginning of Common era.
Extraordinary evidence that Jesus was not only real, but had supernatural powers of any sort. Honestly, if that would be sorcery, that would already be enough to demolish any notions atheists might have.
Buddha is no god and no prophet, but Buddhism describes a world in a way that is incompatible with Christian view, and Buddha is claimed to have a unique revelation about this world that he then passed on before attaining nirvana. So, in a way, he might be seen in the same light as prophets, just not directing to God specifically.
Jesus' birth roughly marks the beginning of the common era. So all of His miracles happened after it began, barring the Virgin Birth if you count that.
But I can still give you sources on Jesus before the common era began. The Jewish prophet Isaiah wrote in 686 BC
"For every boot of the tramping warrior in battle tumult
and every garment rolled in blood
will be burned as fuel for the fire.
For to us a child is born,
to us a son is given;
and the government shall be upon his shoulder,
and his name shall be called
Wonderful Counselor, Mighty God,
Everlasting Father, Prince of Peace.
Of the increase of his government and of peace
there will be no end,
on the throne of David and over his kingdom,
to establish it and to uphold it
with justice and with righteousness
from this time forth and forevermore.
The zeal of the Lord of hosts will do this."
Then further on:
"Awake, awake,
put on your strength, O Zion;
put on your beautiful garments,
O Jerusalem, the holy city;
for there shall no more come into you
the uncircumcised and the unclean.
Shake yourself from the dust and arise;
be seated, O Jerusalem;
loose the bonds from your neck,
O captive daughter of Zion.
For thus says the Lord: “You were sold for nothing, and you shall be redeemed without money.” For thus says the Lord God: “My people went down at the first into Egypt to sojourn there, and the Assyrian oppressed them for nothing. Now therefore what have I here,” declares the Lord, “seeing that my people are taken away for nothing? Their rulers wail,” declares the Lord, “and continually all the day my name is despised. Therefore my people shall know my name. Therefore in that day they shall know that it is I who speak; here I am.”
How beautiful upon the mountains
are the feet of him who brings good news,
who publishes peace, who brings good news of happiness,
who publishes salvation,
who says to Zion, “Your God reigns.”
The voice of your watchmen—they lift up their voice;
together they sing for joy;
for eye to eye they see
the return of the Lord to Zion.
Break forth together into singing,
you waste places of Jerusalem,
for the Lord has comforted his people;
he has redeemed Jerusalem.
The Lord has bared his holy arm
before the eyes of all the nations,
and all the ends of the earth shall see
the salvation of our God.
Depart, depart, go out from there;
touch no unclean thing;
go out from the midst of her; purify yourselves,
you who bear the vessels of the Lord.
For you shall not go out in haste,
and you shall not go in flight,
for the Lord will go before you,
and the God of Israel will be your rear guard.
Behold, my servant shall act wisely;
he shall be high and lifted up,
and shall be exalted.
As many were astonished at you—
his appearance was so marred, beyond human semblance,
and his form beyond that of the children of mankind—
so shall he sprinkle many nations.
Kings shall shut their mouths because of him,
for that which has not been told them they see,
and that which they have not heard they understand.
Who has believed what he has heard from us?
And to whom has the arm of the Lord been revealed?
For he grew up before him like a young plant,
and like a root out of dry ground;
he had no form or majesty that we should look at him,
and no beauty that we should desire him.
He was despised and rejected by men,
a man of sorrows and acquainted with grief;
and as one from whom men hide their faces
he was despised, and we esteemed him not.
Surely he has borne our griefs
and carried our sorrows;
yet we esteemed him stricken,
smitten by God, and afflicted.
But he was pierced for our transgressions;
he was crushed for our iniquities;
upon him was the chastisement that brought us peace,
and with his wounds we are healed.
All we like sheep have gone astray;
we have turned—every one—to his own way;
and the Lord has laid on him
the iniquity of us all.
He was oppressed, and he was afflicted,
yet he opened not his mouth;
like a lamb that is led to the slaughter,
and like a sheep that before its shearers is silent,
so he opened not his mouth.
By oppression and judgment he was taken away;
and as for his generation, who considered
that he was cut off out of the land of the living,
stricken for the transgression of my people?
And they made his grave with the wicked
and with a rich man in his death,
although he had done no violence,
and there was no deceit in his mouth.
Yet it was the will of the Lord to crush him;
he has put him to grief;
when his soul makes an offering for guilt,
he shall see his offspring; he shall prolong his days;
the will of the Lord shall prosper in his hand.
Out of the anguish of his soul he shall see and be satisfied;
by his knowledge shall the righteous one, my servant,
make many to be accounted righteous,
and he shall bear their iniquities.
Therefore I will divide him a portion with the many,
and he shall divide the spoil with the strong,
because he poured out his soul to death
and was numbered with the transgressors;
yet he bore the sin of many,
and makes intercession for the transgressors."
David wrote in 1044BC
"You who fear the Lord, praise him!
All you offspring of Jacob, glorify him,
and stand in awe of him, all you offspring of Israel!
For he has not despised or abhorred
the affliction of the afflicted,
and he has not hidden his face from him,
but has heard, when he cried to him.
From you comes my praise in the great congregation;
my vows I will perform before those who fear him.
The afflicted shall eat and be satisfied;
those who seek him shall praise the Lord!
May your hearts live forever!
All the ends of the earth shall remember
and turn to the Lord,
and all the families of the nations
shall worship before you.
For kingship belongs to the Lord,
and he rules over the nations.
All the prosperous of the earth eat and worship;
before him shall bow all who go down to the dust,
even the one who could not keep himself alive.
Posterity shall serve him;
it shall be told of the Lord to the coming generation;
they shall come and proclaim his righteousness to a people yet unborn,
that he has done it."
My point is not that there should be something before common era - obviously, it's no use searching for account of a person not yet born.
It's rather that they're not contemporary, which puts the same question as to the birth of Caesar - why they, why only then, and how can we be sure of accuracy? Moreover, by then the early Christianity has already developed, so it could just be answering their accounts.
We don't have any contemporary accounts of Alexander the Great either - the earliest account comes 400 years later. While the earliest account of Jesus is from (less than) 20 years after he ascended. That's just history for that time. You'd be hard pressed to have accounts of anybody written in their time. Even Pompeii - which was likely witnessed by 250,000 people, and killed many Roman elite- the earliest account of that is 30 years after the fact.