The muster of the Levites included all the males from a month old and upwards, because they were to be sanctified to Jehovah in the place of the first-born; and it was at the age of a month that the latter were either to be given up or redeemed (comp. Numbers 3:40 and Numbers 3:43 with Numbers 18:16). In Numbers 3:17-20 the sons of Levi and their sons are enumerated, who were the founders of the mishpachoth among the Levites, as in Exodus 6:16-19.

Numbers 3:22 Parallel Commentaries

from a month old. The males of all the other tribes were numbered from twenty years old and upwards; but, had the Levites been numbered in this way, they would not have been nearly equal in number to the first-born of the twelve tribes. Add to this, that as there must have been first-born of all ages in the other tribes, it was necessary that the Levites, who were to be their substitutes, should also be of all ages; and it appears to have been partly on this ground, that the Levites were numbered from a month old and upwards.

Numbers 4:38-40 And those that were numbered of the sons of Gershon, throughout their families, and by the house of their fathers...