Moses would have known. He was the one writing the account. He grew up in Egypt and would have known all about the length of a cubit. And, God filled in the details.
You are missing the point. A modern man went to the site where he thinks he found the Arc, and announced his find was exactly 300 cubits long. WE, as in WE people now living, do not have any idea how long Noah’s cubit happened to be. It is exactly like saying, “Hey, this is exactly as long as Montezuma’s winter blanket”.