That is possible. Lots of people existed back then. Not many gained a reputation for being the son of god, but the part about him having existed is believable.
Yeah, lots of people existed. Just because there was some dude that claimed to be the son of God doesn't mean he was. Just because he preformed, "miracles" doesn't mean he's an angel or whatever. Stories are often exaggerated like this
I just said stories are exaggerated. This Jesus guy might have done great things, yes. And whoever wrote the bible or whatever likely exaggerated those things to such a degree that it was seen as divine.