The Song of the Sea begins with defeat of the Egyptians and ends with YHWH’s enthronement in His temple. Comparison with the Epic of Baal and Enuma Elish clarify the genre and purpose of such hymns, and a striking parallel with Solomon’s prayer in 1Kings 8 offers a clue to the original context of this ancient song.Rabbi Zucker thinks that the Song of the Sea was composed for the dedication of the First Temple at its founding, which is possible. But the song itself, while alluding to a Temple of YHWH, does not mention Jerusalem specifically. (The reference in v. 17 to "the mountain of Your possession" is a mythological term referring to the cosmic mountain and may, but does not necessarily imply Mount Zion.) My teacher, Frank Moore Cross, who is cited in the essay, thought the reference was to the early sanctuary in Gilgal and that the Song of the Sea could have been composed within living memory of whatever event it described. That's possible too, as are a good many other reconstructions. We just don't know.
Frank Moore Cross. "The Song of the Sea and Canaanite Myth" . Pages 112-144 in Canaanite Myth and Hebrew Epic (Harvard University Press, 1973). See note 12 of Rabbi Zucker's essay for a response.