Since Socrates himself never wrote anything down, the only way we know about him now is from the writings of his student Plato. But if that's the case, then how do we know that Socrates was an actual person, and not just a figment of Plato's imagination. Is there any evidence of Socrates independent of Plato's writings.

Plato is not the only ancient author who refers to Socrates. For a quick summary, see this Wikipedia article:

https://en.wikipedia.org/wiki/Socrates

Note the section Socrates as a Figure, which comments on the question you ask.

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