There are two positive mitzvos in the Torah that share certain qualities. Aside from being "Mitzvot Asei," both of them are the only mitzvos in the Torah for which if one does not fulfill them, the person’s soul is subject to kareis - a repercussion which has a number of possible definitions, but minimally could mean to be “cut off” from an eternal connection to God (whatever that might mean). Both of them have blood associated with the fulfillment of the mitzvah. Both of them require preparation in advance. One of them cannot be fulfilled without the other one having been fulfilled. (list is not exhaustive)
The two mitzvos? Bris Milah (circumcision) and Korban Pesach (the Paschal Lamb). It is noted that absent a Beis HaMikdash we don’t fulfill the Korban Pesach, so some of the connections are less relevant in our time.
Rashi (12:6) quotes verses from Yechezkel 16 which describe metaphorically God’s turning Jerusalem into a presentable city, including stating “And I passed by you and saw you downtrodden with your blood, and I said to you, 'With your bloods, live,' and I said to you, 'With your bloods, live.'” Many Midrashim say the plural form of ‘bloods’ indicates that blood of the Paschal lamb and circumcision blood were combined and placed on the doorposts in Egypt to serve as a double protection for the Hebrews during the final plague.
Rashi says the circumcisions in Egypt took place at night, seemingly contradicting the Midrash that the bloods were combined. The instruction for the slaughtering of the lamb and putting the blood on the doorpost is in 12:6-7, making clear that not much time passed between the two actions. People were indoors at night; circumcision blood could not be put on the doorpost!
The great irony of this is that the idea that an ערל, an uncircumcised male, can’t partake of the Korban Pesach, seems to be an afterthought first mentioned in 12:48, basically the last instruction given to Moshe to tell over to the Israelites.
Rabbenu Bachaye writes וזה יכלול שנמולו כלן ועשו את הפסח, which can certainly be understood to mean the two actions were done in that order: first Milah and then slaughtering the Pesach. Which could also lead us to suggest that, rather than an afterthought, the last thing Moshe heard – the instruction for Milah – was freshest in his mind, and therefore what he mentioned first to the Bnei Yisrael.
Rashi’s explanation leaves more questions than answers in light of the halakha based on the verse וביום השמיני ימול בשר ערלתו, that a Bris must take place during daylight hours, from sunrise to sunset, even if done after the 8th day. (Pesachim 4a, Yoma 28b). Comes Rabbenu Bachaye with the save… what do you think?