It's clear from the mishnayos in the eighth chapter of B'choros[1] that one is capable of redeeming his firstborn son before the latter is a month old. (For example, they discuss whether the kohen must return the redemption money if the baby died after the redemption before the baby turned a month old.)
Considering the redemption celebrations that people make on such an occasion nowadays[2] in the United States, and considering that sometimes it would doubtless be more convenient to hold such a party on one day than on another for a variety of reasons, I'm surprised that I've never heard of a redemption being held early. Why not?
[1] I haven't studied that g'mara.
[2] Not right now, during the COVID-19 epidemic, but more generally.