Only from a purely rational POV:

As far as I know the following can be stated as historical
truths:

1. 'Yoshua' was a common name there and then, like 'John' in
our days.
2. Messiah's were coming and going; it was not a very rare
phenomenon.
3. Crucifixion was a common punishment; many Jews and
others were crucified for lots of reasons.
4. A religion (Christianity) came into existence in the first
century, centred (from hearsay) around a man called
Yoshua/Jesus of Nazareth. This religion spread like fire.

Conclusion:

It is very likely there was a man around 30 C.E. :

1. who was called Yoshua or in Greek Jesus,
2. who came from Nazareth,
3. and who was called messiah by other people,
4. and who was crucified by the Romans.

This is no hard proof; but I'd say on the basis of this it will be
harder to proof such a man can never have existed there and
then.

From a purely rational pov it is completely reasonable and
acceptable to assume such a man has existed.

Having faith (him being 'the son of God' etc.) is a different
matter imo. Scripture is more than writings that look into the
past. Faith is not just subscribing a list of historical truths.

Aad