One final point regarding פרשת בא. Many do not realize that not only did the Jewish people deal with the קרבן פסח and place its blood on the door posts, but they also were involved with the Mitzva of ברית מילה. The nation needed to be involved with circumcision. Without ברית מילה, they could not partake of the קרבן פסח.
The blood of circumcision was also placed on the door posts. This is why we mention בדמייך חיים, with the blood you shall live, is said twice as part of the ברית מילה ceremony.
It is also interesting that the only two positive Commandments mentioned in the Torah for which one receives a punishment, is for not offering the קרבן פסח or performing ברית מילה. The punishment is כרת, or being cut off from the Jewish people, a very harsh punishment.
In essence, we became a nation at that time and this was part of the conversion process.