Of course the answer would be no, you wouldn't believe a stranger just because he said he was Jesus, or the Messiah, or any manifestation of a god, or even a special messenger like an angel. In fact, you'd probably assume that he was either joking or in need of care and medication. It would take an extraordinary amount of evidence to convince you otherwise, unless you are unfortunately suggestible or extraordinarily gullible.
You would almost certainly dismiss even a miracle like turning water into wine as a conjuring trick and the chances are if he touched a blind person and restored their sight you would assume they were in collusion. With some justification you'd start to suspect a scam. Any moment now he's going to ask me for a donation so he can concentrate on his mission and not have the 'distraction' of having to work for a living.
And yet you're expected to take second hand (at best) accounts of a man doing just that in biblical times on faith, and not ask for evidence. In fact, you're expected to be proud of 'accepting Jesus on faith' as though it's something to be proud of; a virtue even!
Yet, reading the Bible, what was it that allegedly convince the disciples that Jesus was the Messiah and God incarnate? Was it 'on faith'? Was it because he walked up to them, a total stranger, and said, "Hi! I'm Jesus, Son of God!"?
Nope, it was allegedly evidence in the form of miracles which did it. Even Abraham, the founder of three major world religions and countless minor sects, needed evidence, as did Moses. All the writers of the New Testament cite evidence and Paul even performed miracles (albeit small ones like turning a stick into a snake and back) to convince people.
So, why did Jesus' chosen disciples and all those Old Testament prophets have less faith that you are expected to have? Why was it okay for biblical saints to require evidence and rely on science (if you believe the stories) to arrive at their beliefs, but not you?
The answer is quite simple, of course, they wrote about having seen the evidence but they had none to show, so they fell back on the ruse of telling you it was good not to require evidence; that God would be upset if you asked for it; that 'faith' is a virtue and something to be proud of. Not that they ever doubted or needed evidence, obviously. Oh, no!
Pah! That Doubting Thomas, eh? Oh! Ye of little faith!