You can see by reading the entire Chapter 3 of Numbers, especially verse 7, that GOD chose the tribe of Levi to "do the service of the temple", rather than to assign first-born sons of all the tribes of Israel to do the service of the temple.
This does not mean that first-born sons were no longer dedicated to GOD, nor had any other way to serve GOD.
So to answer your question, because Jesus was a first-born son, he was dedicated to GOD, and his mission had nothing to do with the service of the temple, but rather to be a Prophet and a spiritual High Priest, at least at his first coming, and then a world ruling King at his second coming, and it was directly stated by the angel Gabriel to Mary that her son Jesus would be this prophesied son of David / King of Israel: "He will be great, and he will be called the Son of the Highest; and the Lord God will give him the throne of his father David. And he will rule over the house of Jacob for ever; and there will be no limit to his kingdom (Luke 1)."
I hope you feel this answers your question.