Can a Bar Mitzvah boy be Chazan on the eve of his Bar Mitzvah?
Can my son be Chazan on the Maariv of his Bar Mitzvah, or does he need to wait until the next day?
Yes he can, as long as Maariv starts after the Zman, i.e., nightfall.
Shulchan Aruch Alter Rebbe 53:13
PS. I do want to comment however that the Rebbe is not in favor of having Bar Mitzvah boys Davening as Chazan on the day of their Bar Mitzvah.
אף שכנראה נהגו כן בכ״מ, וכ״מ ממג״א רכה, ד: כשהנער מתפלל – ראה מענה ח׳ ניסן תשכ״א, נדפס בבית משיח גל׳ 457.