“When the LORD finished speaking to Moses on Mount Sinai, he gave him the two tablets of the covenant law, the tablets of stone inscribed by the finger of God.”
Read a little further.
When Moses came down from Mount Sinai he saw the Israelites worshiping the golden calf and threw the tablets down and they shattered.
Moses then made a copy of the tablets that God had written and that is what was placed in the Ark of the Covenant.
So, if they found the Ark and it contained the tablets they would have been written by Moses.
It occurs to me that there must be fragments of the original tablets still on Mount Sinai. Looking for them might be an interesting archeological expedition.