The Levites were in a class of their own. They hadn’t made any specific offering to dedicate the tabernacle. Instead, their whole lives were set aside for God’s service as a special offering to the Lord.
The reasoning went back to events in Egypt:
Numbers 8:16-17 “Of all the people of Israel, the Levites are reserved for me. I have claimed them for myself in place of all the firstborn sons of the Israelites; I have taken the Levites as their substitutes.For all the firstborn males among the people of Israel are mine, both of people and of animals. I set them apart for myself on the day I struck down all the firstborn sons of the Egyptians.
On a practical note, they weren’t taken out of the community altogether:
Numbers 8:24-25 This is the rule the Levites must follow: They must begin serving in the Tabernacle at the age of twenty-five,and they must retire at the age of fifty.
It meant the Levites still had strong young men around their households to do the heavy work that would have been needed at the time.