Verse 51, where it says "and it came to pass the selfsame day that the LORD did bring the children of Israel out of the land of Egypt by their armies," is positioned at the end of this paragraph that begins in verse 43. That does not mean that they were circumcised "the selfsame day," but rather that verse is a reference back to verse 41: "And it came to pass at the end of the four hundred and thirty years."
At this point (verse 51) in the story of the events that took place in Egypt, the males had already taken the Passover, and therefore the men were already circumcised. They couldn't have taken the Passover, which occurred at the beginning of chapter 12, unless they had been circumcised. So this section then, from verse 43 through 51, is a reminder of a command given earlier. They didn't get circumcised after Passover and then immediately get up and leave Egypt within the same few hours period.
So at nightfall, at the beginning of the Days of Unleavened Bread, they went out.
So proposal number two is being accomplished on the first day of Unleavened Bread. He not only freed them from the hand of the Egyptians, He brought them out on the very first day of Unleavened Bread.
A little review: how much has Israel done so far? Not much, not much at all. They came out of the literal state of Egypt in one day, not seven. One day they were out of Egypt, but they were still within the territory that was under the sovereignty of Egypt, much the same way that we might consider the metropolitan area of a city. They were out of Egypt at the very beginning and at this point, it is almost entirely a work of God.
So we see the same language here. They went out on the fifteenth. And verse 22, of this chapter, proves that none of these verses (17, 41, or 51) could refer to Passover day because (in verse 22) they had to stay in their houses until morning. They were still in their houses when daylight of the fourteenth came, and they had not even gone to Rameses yet.
This verse attributes Israel's release, and thus ours too spiritually, entirely to God. All Israel had to do was to choose to leave and to literally walk out. But even here God made the choice fairly easy by painting such an attractive picture of the future that they could hardly resist. The same principle happens to us.
