Or HaChaim on Numbers 3:15/אור החיים על במדבר ג׳:ט״ו

1 כל וכר מבן חודש ומעלה, every male above the age of one month. The reason the Levites were counted from the age of one month is that they replaced the firstborn who also were viable at the age of one month. The reason the firstborn had to ransom himself was that a Levite was going to take his place and he had to redeem himself from his former obligation, i.e. sanctity, an obligation which was due to his birth as a firstborn. You may well ask why the firstborn Levites nowadays do not have to redeem themselves. The reason is that the Levites who replaced the firstborn at that time had been appointed by G'd to replace the firstborn of all future generations. Their sanctity was of a permanent nature. Perhaps the Torah alludes to this with the repetition of the words in verse 12: הנה לקחתי את הלוים….והיו לי הלוים. "I have taken the Levites….and the Levites shall be Mine." The second word הלוים seemed redundant otherwise.