The Book of Mormon is convincing evidence of the Restoration.

1 Nephi 13: 40 And the angel spake unto me, saying: These last records, which thou hast seen among the Gentiles, shall establish the truth of the first, which are of the twelve apostles of the Lamb, and shall make known the plain and precious things which have been taken away from them; and shall make known to all kindreds, tongues, and people, that the Lamb of God is the Son of the Eternal Father, and the Savior of the world; and that all men must come unto him, or they cannot be saved.

The prophet Gordon B. Hinckley explained it best when he said:

“If the Book of Mormon is true, the Church is true, for the same authority under which this sacred record came to light is present and manifest among us today. It is a restoration of the Church set up by the Savior in Palestine. It is a restoration of the Church set up by the Savior when he visited this continent as set forth in this sacred record.
“If the Book of Mormon is true, the Bible is true. The Bible is the Testament of the Old World. The Book of Mormon is the Testament of the New. The one is the record of Judah, the other is the record of Joseph, and they have come together in the hand of the Lord in fulfilment of the prophecy of Ezekiel. Together they declare the Kingship of the Redeemer of the world, and the reality of his kingdom” (in Conference Report, Oct. 1959, 119).
“We are to use the Book of Mormon in handling objections to the Church. . . .
“. . . All objections, whether they be on abortion, plural marriage, seventh-day worship, etc., basically hinge on whether Joseph Smith and his successors were and are prophets of God receiving divine revelation. Here, then, is a procedure to handle most objections through the use of the Book of Mormon.
“First, understand the objection.
“Second, give the answer from revelation.
“Third, show how the correctness of the answer really depends on whether or not we have modern revelation through modern prophets.
“Fourth, explain that whether or not we have modern prophets and revelation really depends on whether the Book of Mormon is true.
“Therefore, the only problem the objector has to resolve for himself is whether the Book of Mormon is true. For if the Book of Mormon is true, then Jesus is the Christ, Joseph Smith was his prophet, The Church of Jesus Christ of Latter-day Saints is true, and it is being led today by a prophet receiving revelation.

Under the direction of Jesus Christ, the priesthood and the Church were restored through His servants.

Acts 3:20 And he shall send Jesus Christ, which before was preached unto you:
21 Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.

HE'S TALKING ABOUT A RESTORATION AFTER CHRIST LEFT!
Protestant Christian belief is that the original church had fallen away after the death of the apostles, which we can see evidence of in these records. Not only that, but the record talk about everything being restored at a later time!

D&C 13:1 Upon you my fellow servants, in the name of Messiah I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins; and this shall never be taken again from the earth, until the sons of Levi do offer again an offering unto the Lord in righteousness.

I have a sure testimony of the Priesthood and its power and authority to act in the name of God. As such, it most assuredly must be concluded that Jesus was and is the Christ, that the priesthood was restored to Joseph Smith, that Joseph Smith was a true prophet, and that this is God’s true church on the earth today.

If God really cared enough to do all of this, then God will doubtlessly care enough to tell any that ask Him if He really did it. It's the only way to know for sure.