Albert Barnes Commentary Exodus 19:1-2

"In the third month after the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai. And when they were departed from Rephidim, and were come to the wilderness of Sinai, they encamped in the wilderness; and there Israel encamped before the mount." — Exodus 19:1-2 (ASV)

The wilderness ... the desert of Sinai - If the mount from which the law was delivered is the rock of Ras Safsafeh, then the spacious plain of Er Rahah would be the “desert” of Sinai .