If the Priesthood is the power of God given to men on earth, why was it not restored first? Wouldn’t this power and authority be required to substantiate the restoration of the gospel?
Priesthood is power and authority. People can, and do, accomplish many great things with divine assistance (or “power”) without ever receiving a priesthood ordination–indeed, without ever having been properly baptized. What priesthood provides is authority, in addition to an additional degree of spiritual power (D&C 84:33-40).
As the Restoration progressed, Joseph Smith found himself in a situation where he was being invited to exercise authority over others–sometimes people merely asked him to obtain revelations on their behalf; but at other times he received revelations affirmatively instructing third parties to act in a particular manner in order to facilitate the work (Martin Harris, for example). In the spring of 1829, as the work of translating and publishing the Book of Mormon came to a head, Joseph Smith received the Aaronic Priesthood on May 15 of that year. By the time that the Church was organized on April 6, 1830, Joseph Smith and Oliver Cowdery held sufficient priesthood authority to preside over it and priesthood power to carry out the tremendous work that still lay ahead of them.