In no way does the Church consider the crossing of the Red Sea a kind of 'baptism' as a sign of God's covenant with the Jews. That sign was/is circumcision.
1 I do not want you to be unaware, brothers, that our ancestors were all under the cloud and all passed through the sea, 2and all of them were baptized into Moses in the cloud and in the sea. 3All ate the same spiritual food, 4and all drank the same spiritual drink, for they drank from a spiritual rock that followed them, and the rock was the Christ.
A spiritual rock that followed them: the Torah speaks only about a rock from which water issued, but rabbinic legend amplified this into a spring that followed the Israelites throughout their migration. Paul uses this legend as a literary type: he makes the rock itself accompany the Israelites, and he gives it a spiritual sense. The rock was the Christ: in the Old Testament, Yahweh is the Rock of his people (cf. Dt 32, Moses’ song to Yahweh the Rock). Paul now applies this image to the Christ, the source of the living water, the true Rock that accompanied Israel, guiding their experiences in the desert.