'Wrote' in the Bible

He declared to you his covenant, which he commanded you to observe the Ten Commandments that he wrote on two stone tablets.

Then the LORD inscribed on the tablets what he wrote before, that is, the Ten Commandments that the LORD declared to you on the mountain from the middle of the fire during the day of the assembly. And the LORD gave them to me.

Then Moses wrote down this Law and gave it to the Levitical priests who carry the Ark of the Covenant of the LORD and to all of Israel's leaders.

So Moses wrote the song that very day and taught it to the Israelis.