If you have a chance to strengthen your Emuna with stories of Gedolim and Nissim, or with proofs, how can you turn it down!?
Simple. I was not put here to be a Malach. The One who put me here wanted me to be a person, with nisyonos. If Emunah was so obvious, there would be no nisayon.
As far as the OP, I don’t see any need to prove. First prove that you are a person (and not a figment of someone’s imagination) and then we can discuss Maamad Har Sinai 🙂