score:2
1983 can. 1031 ยง1 (=1917 can. 975 ยง1) says one must be at least 25 to be ordained licitly (legally):
The presbyterate [priesthood] is not to be conferred except on those who have completed the twenty-fifth year of age and possess sufficient maturity
Validity requires a baptized male, 1983 can. 1024 (=1917 can. 968), so technically a baptized male baby could be validly ordained a priest, but doing so would break canon law.
Just as the Church has the authority to establish impediments to contracting marriage (cf. Council of Trent session 24 can. 3 & 4), so, too, can she legislate the canonical age for receiving Holy Orders.
The Church has this legislative authority because Matrimony and Holy Orders are the two sacraments "intended for the perfection of the multitude", not primarily "for the perfection of the individual"; Holy Orders remedies "divisions in the community", and matrimony remedies "the decrease in the population that results from death" (Summa Theologica III q. 65 a. 2 co.).
Upvote:2
Holy Orders is a call to a specific role in the church. The role includes providing spiritual counsel, church leadership, presiding at Mass, instructing the faithful, hearing confession. None of these can be done by a baby.
Not all Catholics are called to be priests. Even the most faithful and devout may be called to some other role. Deciding if someone is called to be a priest cannot be done while they are still a baby.
Being a priest requires knowledge and training, and people do not receive Holy Orders until the training is complete. If someone were ordained as a baby, even when they grew to adulthood but before they were trained they would technically be permitted to carry out all the above roles but would not have the ability to carry them out effectively.