As far as I can remember, the books don't really analyze this question. However, there are a few points that may have helped Harry believing Hagrid:* Hagrid's personality may have helped.
* Hagrid himself is "unbelievable", being a half-giant.
* Hagrid did some magic himself.
* The letter from Hogwarts.
* Uncle Vernon's reaction to Hagrid wanting to tell Harry the truth.
* Harry's previous experiences with magic (he had accidentally done magic, now and then).
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Rubeus Hagrid.
Hagrid decided to buy Harry's animal and gift it to him as a birthday present. Hagrid is allergic to cats as they make him sneeze and Toads were old fashioned, students would have laughed at and made fun of Harry and Hagrid didn't want that
The Actor Robbie Coltrane portrays the character Hagrid in the Harry Potter Film Series.
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Lily Luna Potter, Harry's daughter, would have grown up knowing because all her family would be magical. Lily Evans, Harry's mother, was told by Severus Snape and it was confirmed by her Hogwarts letter. Somebody would have come and explained it to her parents like Hagrid did with Harry (only they thought he knew).