By way of parallel, God is missing from the Megillah and from Shir HaShirim.
Preachers and teachers find both phenomena highly fascinating.
The consensus of opinion is that an unseen presence is so evident that it hardly needs a mention by name. In Moses’ case there could not have been an Exodus without him.
Yet the Haggadah not only takes him for granted but deliberately moves the credit and emphasis to the Almighty. God brought the redemption – “not by an angel, nor by a seraph, nor by a messenger”.
Something must be happening that is not immediately obvious. It is not merely that the Haggadah wants us to know that nothing ever happens without God pulling the strings. The phrase “pulling the strings” hints at a tension between Divine and human activity.
We can’t be certain who redacted this part of the Haggadah, but it could have been at a time when Christianity was building up the status of Jesus and Judaism had to respond by playing down the level of human leadership.