Chabad.org — English translation + Rashi
Torah Temimah on the firstborn claim: “כי לי כל בכור” — the consecration of the firstborn at the time of the Exodus is the legal and historical basis for substituting the Levites.
English: “For every firstborn among the children of Israel is Mine, both man and beast” — on the day I struck every firstborn in the land of Egypt I consecrated them to Myself.
Historical-legal linkage — the Exodus event itself creates the permanent claim that is later transferred to the Levites.
The substitution of Levites for firstborn is not an arbitrary administrative choice; it rests on the original Divine claim established at the plague of the firstborn.