Those that understand and accept the idea of the Great Apostasy, must also embrace the idea of a restoration as well. If the Church were taken from the earth, then at some point in the latter days, it will be restored again to the earth. This restoration is not an incremental improvement of a corrupted Church, but rather the establishment of a completely new organization, brought forth by the Lord himself through the calling of new, modern-day prophets. The problem for the last two centuries is that no one has said Restore!
22 But this is a people robbed and spoiled; they are all of them snared in holes, and they are hid in prison houses: they are for a prey, and none delivereth; for a spoil, and none saith, Restore.
For a restoration of the Church and Kingdom of God to occur, the Lord will need to call prophets. In fact, without using a prophet to transmit his will to the children of the earth, the Lord will basically do nothing.
7 Surely the Lord GOD will do nothing, but he revealeth his secret unto his servants the prophets.
After Jesus Christ was resurrected, he appeared unto many of his disciples, including his chosen Apostles. He made it clear in these encounters that he was not a gaseous cloud or spiritual being, but rather he had a physical body of flesh and bone.
36 ¶ And as they thus spake, Jesus himself stood in the midst of them, and saith unto them, Peace be unto you.
37 But they were terrified and affrighted, and supposed that they had seen a spirit.
38 And he said unto them, Why are ye troubled? and why do thoughts arise in your hearts?
39 Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
40 And when he had thus spoken, he shewed them his hands and his feet.
41 And while they yet believed not for joy, and wondered, he said unto them, Have ye here any meat?
42 And they gave him a piece of a broiled fish, and of an honeycomb.
43 And he took it, and did eat before them.
If Jesus could appear to his prophets and apostles in ancient times, then we should expect him to do the same today, if he desired to do so. The scriptures indicate that indeed he will appear to a new prophet when he restores Zion to the earth.
16 When the LORD shall build up Zion, he shall appear in his glory.
17 He will regard the prayer of the destitute, and not despise their prayer.
From these verses in the Psalms, we learn that a clear marker of the restoration of Zion is that he will appear in his glory to someone. Latter-day Saints know this someone to be Joseph Smith, and the location of this visit was the Sacred Grove in Palmyra, New York. The full account of this first encounter with the risen Lord in modern times can be had in Joseph Smith History in the Pearl of Great Price, which is a book of scripture had by the Church of Jesus Christ of Latter-day Saints. This vision occurred in the morning of April 6, 1820.
25 I have raised up one from the north, and he shall come: from the rising of the sun shall he call upon my name: and he shall come upon princes as upon morter, and as the potter treadeth clay.