Parashas Bamidbar
וְזֹ֣את ׀ עֲשׂ֣וּ לָהֶ֗ם וְחָיוּ֙ וְלֹ֣א יָמֻ֔תוּ בְּגִשְׁתָּ֖ם אֶת־קֹ֣דֶשׁ הַקֳּדָשִׁ֑ים אַהֲרֹ֤ן וּבָנָיו֙ יָבֹ֔אוּ וְשָׂמ֣וּ אוֹתָ֗ם אִ֥ישׁ אִ֛ישׁ עַל־עֲבֹדָת֖וֹ וְאֶל־מַשָּׂאֽוֹ׃
Do this with them, that they may live and not die when they approach the most sacred objects: let Aaron and his sons go in and assign every one of them, in turn, to his duties and to his porterage.
Torah Temimah points to TT (verified).
איש איש על עבדתו — מכאן שאינו נכנס לעבודה עד שיגדל ויהיה לאיש.
English: “Each man to his work” — from here [we learn] that one does not enter the service until he has grown and become a man.
Custom
Chazal derive that Levitical service begins only when one has reached full manhood.