two elements of geirus

Rashi in parshas Bo quotes a hava amina that a ger should bring a korban pesach right after he converts and not wait until pesach.  A few weeks ago my son explained that we see from Rashi that the korban pesach in Mitzrayim was a kiyum not just of the pesach offering, but also a kiyum of a korban geirus, and therefore one could have a hava amina that every ger bring such a korban at the time of conversion.  Similarly, the milah done before pesach Mitzrayim was also a kiyum in geirus, as the mitzvah of milah itself had already been given to Avraham Avinu.

I was not so enamored with this idea.  The gemara learns the need for a korban for geirus from the korban offered at the time of mattan Torah (end of our parsha).  Tevilah and milah are also learned from mattan Torah.  Why would Klal Yisrael need another geirus at mattan Torah, I asked him, if they already had a geirus in Mitzrayim?

My attempt to answer my own question:

Usually a ger has milah first and then tevilah.  Ramban (Yevamos 47) holds that bdieved it can be done the other way around as well.  Both milah and tevilah are steps in the geirus process, and until both are complete, in whatever order, the geirus in incomplete.

Achronim ask: the gemara (Yevamos 97) writes that if a mother pregnant with twins converts, even though ger she'nisgayer is k'katan she'nolad and all former familiar relationships are null and void, her sons born as Jews are considered related as brothers and there would be an issue of eishes ach for one to marry the other's wife.  Why should this be true according to Ramban?  Even though the twins are yotzei tevilah of geirus in utero, they still need milah to complete their geirus.  8 days after they are born, when they have milah and become geirim, their relationship with each other should be void?

Similarly, the gemara (Bechoros 47) writes that if a pregnant woman converts, the baby is a bechor l'kohen.  According to Ramban, the baby is not even Jewish at birth!   Since milah is necessary for complete geirus, it is only on day 8 that the baby even becomes Jewish, and therefore should not be considered a bechor?

R' Naftali Trop (shiur on ger katan in Kesubos) answers that there are two stages of geirus.  Ramban does not mean that before milah the child is an aku"m.  The child is a member of the Jewish nation, he is related to his Jewish brother, he is a bechor l'kohen if he is the first baby to come out of his mother's womb.  However, the child lacks a kedushas yisrael.  That is missing without the added step of milah.  

How could there be geirus for children at mattan Torah when geirus requires daas and a katan has no daas?  The answer is that the children were already part of Klal Yisrael since they were bnei Avraham, Yitzchak, and Yaakov.  What the geirus of mattan Torah added is the element of kedushas yisrael.  That extension of the geirus, of what it means to be part of Klal Yisrael, does not required additional daas or consent to be accepted.

I suggested to my son that perhaps this is why there was a to stage process of geirus, one in Mitzrayim and one at mattan Torah.  The first, in Mitzrayim, forged us into a nation.  The second, at mattan Torah, forged a kedushas yisrael, which is only possible through Torah.  Without that we might have been a distinct nation, separate from Mitzrayim, but we would have not been a holy nation.