“זֶ֤ה אֵלִי֙ וְאַנְוֵ֔הוּ This is my God and I will glorify Him” (Exodus 15:2)
“This” means they pointed, explains Rashi.
Who among the newly-freed slave would have known what God looked like in order to recognize God at that moment?
Not Moses, women.
Women who were afraid to give birth in Egypt lest their newborn be thrown into the sea, went out to the fields to give birth under the trees. To assist them in those difficult conditions, “The Holy Blessed One descended from heaven and cared for them and the newborn as a midwife would do.” (Babylonian Talmud, Sotah 11:b).
Therefore, when the Red Sea split they recognized the Saving Power who had attended them as a midwife.
But if you check a standard printed or online Talmud, you find that quote is slightly different: “The Holy Blessed One sent someone from heaven to care for them and the newborn as a midwife would do.” (Babylonian Talmud, Sotah 11:b).
Not God himself but a messenger. Apparently, a later scribe or editor was deterred by the concreteness of the original description and toned it down.
After God is identified comes “glorify God.”
How can we glorify God? The sages offer various answers, but I want to focus on the one given by Abba Shaul, “Be like God, just as God is merciful, you should also be” (Mekhilta 15:B).
In attitude and in deeds, as Rabbi Chama said Rabbi Hanina explains elsewhere:
Because God clothes the naked... you, too, should clothe the naked.
God visits the sick.... you, too, should visit the sick.
God comforted mourners.... you, too, should comfort mourners.
God buries the dead .... you, too, should bury the dead: (Babylonian Talmud, Sotah 14: a)
Here we have three different ways (but not contradictory) to experience the divine presence in the world:
Directly, mediated by the loving kindness we receive from others, and actively by helping others.
Only the last is in within our control.
When we feel helpless against the forces of evil (Pharaoh) or chaos threatens to either side (the water standing on either side when crossing the Red Sea), when our way to “This is my God” is blocked, we can still live in the loving kindness we want to see and feel the world.
That depends on us alone, and it holds within it the hope of making God's presence felt in the world.
 “A maid-servant at the sea saw more than Isaiah, Ezekiel and all the other prophets.” Mekhilta Beshalach 3.
 According to the manuscripts, see Joshua Levinson, The Twice-Told Tale, page 299. I thank Dr. Gila Vachman, of the Schechter Institute and Project Zug for the reference.
 Heavenly or human? Does it matter? See Parashat Vayeshev: Humans and angels.
 Or by the fact that the sages, who always spoke about God using masculine language, here attribute to God a clearly feminine role.