I think if I were a time traveller trying to convince you, I would travel to some time when you were alive, but not fully conscious or able to remember. I'd pick out details about your life that you would not remember, but that your mother would remember. Lets say, some idiosyncrasy or affectation you had as a child, the clothes you wore on your first day of school, detail about how you used the house you lived in before you moved when you were 2...This wouldn't be trivial but if I had a time machine and some researching ability, and some social skills, I'm confident I could come up with a good detail.

I would then predict that that was the case, and I would show you photo ID of who I am and that your mother doesn't know me. Then I'd ask you to call your mother and ask her about the facts. You could even ask her about me and if she knew me, describe me physically... Hopefully the detail is one only she would know.

I'd say it would be unreasonable to not believe me after that, I think you'd have to believe that your mother was in on the ruse.