It was Moses who first put up the Tent of Meeting—poles, curtains, covers, and everything inside. He couldn’t have possibly put the tent up by himself. The Levites would have helped him with the parts they were allowed to help with; but Moses was responsible as supervisor. He got the credit and the great responsibility:
Exodus 40:16 Moses proceeded to do everything just as the Lord had commanded him.
The reward for moses and all the Israelites was that, when Moses had finished, God moved in.