Targum Pseudo-Jonathan keeps one detail from the Hebrew and clarifies another. Miriam, the sister of Aaron, is called the prophetess. She takes a tambourine, and all the women come out after her, dancing with tambourines and playing on instruments.
Notice the Targum's careful word choice. Miriam is neviata, the prophetess, not merely Aaron's sister. The Sages read this title closely and understood that her prophetic office predated the Exodus itself. According to the <a href='/categories/midrash-aggadah.html'>aggadic tradition</a> (developed in Sotah 12b-13a of the Babylonian Talmud, compiled c. 500 CE), Miriam had prophesied while still a young girl in Egypt that her mother would bear a son who would redeem Israel. She had been waiting at the Nile to see the prophecy fulfilled when Pharaoh's daughter lifted Moses from the water.
So when she picks up the tambourine at the sea, she is not improvising. She had been rehearsing this song since childhood. The Targum underlines the detail: all the women came out after her. Not a few. All. The women of Israel had carried tambourines out of Egypt on the chance that one day they would need them for a song like this.
The Maggid holds this image a moment longer than necessary. Faith, he says, is carrying a tambourine out of slavery. It is packing for a miracle you have not yet seen. Miriam led because she had been ready the longest.
The takeaway: prepare the instruments of joy before you have a reason for them. The song may arrive faster than you think.