The following is from a mild, Partial-Preterist perspective, seeing an at-face-value fulfillment of Daniel and and most of Revelation in approximately the period of 50 AD - 350 AD.
The Simple Answer
The Rock is the Kingdom of God.
In the time of those kings, the God of heaven will set up a kingdom
that will never be destroyed, nor will it be left to another people.
It will crush all those kingdoms and bring them to an end, but it will
itself endure forever. This is the meaning of the vision of the rock
cut out of a mountain, but not by human hands—a rock that broke the
iron, the bronze, the clay, the silver and the gold to pieces.
So, that the Rock is the Kingdom is, of course, the most obvious answer. So, in answer to your question,
What is this little rock that is so marvelous[?], that would be it. But, the greater question, which it is assumed you are asking, is, then,
What is the Kingdom of God?
What is the Kingdom of God?
Fortunately, someone else asked that exact question.
Then Jesus asked, "What is the kingdom of God like? What shall I compare it to?
Again he asked, “What shall I compare the kingdom of God to?
Luke 13:18, 20
His answer was as follows.
It is like a mustard seed, which a man took and planted in his garden.
It grew and became a tree, and the birds perched in its branches.
It is like yeast that a woman took and mixed into about
sixty pounds of flour until it worked all through the dough.
Luke 13:19, 21
So, considering Jesus' answer to this very question, I would claim that it would be faith in the heart of a believer and the internal dwelling of the Holy Spirit.
Physical or Spiritual?
The subject comes to one issue, is the Kingdom that was promised to be physical or spiritual. While some contend either or, and some attempt "both", I would say "spiritual". Consider the evidence.
In Mark 1:15, Jesus said the time was fulfilled, and the Kingdom was at hand. Since this was a time statement, it seems hard to extract any additional substantial length of time from this, and put the Kingdom as "yet to come".
In Matthew 6:10, we see Jesus' modeled prayer saying, "Your Kingdom come ... on earth as it is in heaven." Here, we see that the request is that the already existing Kingdom ("your kingdom", speaking to the Father), would come to Earth. That is, the Kingdom is in heaven, and we want something to happen. This positively identifies the Kingdom as in existence, we are praying for what already is there to be here.
In John 18:36, Jesus said His kingdom was not of this realm, or world. Some point to the last phrase which reads, "But now my kingdom is not of this world", and suggest that the "now" indicates that while it is not currently of this world, it will be someday. It is interesting to note that the NASB renders this as "but as it is, my kingdom ...". Regardless of this technicality, however, Jesus said that then, at least, the Kingdom was spiritual, regardless of the possibility of any future form.
Scriptures such as Matthew 12:28 are indicative of the then presence of the Kingdom, speaking of His deliverances.
The Origin of the Kingdom
If the Kingdom, then, was spiritual in Jesus' day (Matthew 6:10; John 18:36, and many others), and the prayer in Matthew 6:10 was to bring what was spiritual into the Earth, what then is the nature and origin of this Kingdom?
In Matthew 25:34, we read, `inherit the kingdom prepared for you from the foundation of the world.' From this, we understand that the Kingdom has been in existence from the foundation of the world, and hence, therefore it (a) exists and (b) is spiritual (since the foundation of the world is the foundation of all things physical).
Then, in Psalm 145:13, we see "Your Kingdom is an everlasting Kingdom". So, we see that the Kingdom will last forever, everlasting (no end), not eternal (no end or beginning).
Now, if one holds that the literal Heaven and Earth will be physically destroyed, and that the "New Heaven and New Earth" are to be completely "New", then you have a problem. For this to hold, and to have a physical Kingdom of God in the future, the Kingdom begins as spiritual, becomes natural, and must becomes spiritual again to last through the renovations. Moreover, that which was spiritual is made earthly, and then spiritual again, so regardless of which you think is better, it will have to be "degraded" in one of those moves.
Further, it was this Kingdom that Israel had possessed at some time in the past. In Acts 1:6, the disciples asked if Jesus would at that time "restore" the Kingdom to Israel (not to them personally, as they seem to have had it already in Luke 22:29--they asked about the whole nation).
When Jesus, therefore, said the Kingdom was "at hand", he was not speaking of its "inauguration", but its "proximity". Likewise, when Jesus spoke of Himself coming in that Kingdom at the end of the age (world), the focus is again not on the "Kingdom", but on its "coming". From the perspective of man and this soon-to-pass-away Earth, we may see this as a "consummation", but from the perspective of the Everlasting Kingdom, as Jesus put it, it is just a matter of gathering up the tares for burning, and getting the wheat into the barn. Not much changes from that perspective, because the Kingdom was complete long ago.
Is There a Clear Promise of a Physical Kingdom?
In my opinion, the answer is no. The promise is to David's throne. But, the interesting thing about this prophecy is it involves David's heir, Solomon. God begins promising David that his throne and house would endure, and then switches to Solomon's son, then finishes with David. Thus, the promise to Solomon secures the promise to David.
However, if Jesus were to sit merely on the throne of a man, then David would be superior to Jesus. But, Jesus is the root and offspring of David. Thus, when David sat on his throne, he was really sitting on the throne of Jesus, the throne of God. So, we see that this promise to David is securing the promise to Jesus from the Father, in the same way that the promise to Solomon secured Davids. Thus making Jesus the greater, because David sat on His (Jesus') throne.
This is borne out in four verses in Chronicles. 1 Chronicles 28:5; 1 Chronicles 29:23; 2 Chronicles 9:8; 2 Chronicles 13:8. In these four places, the throne or kingdom of David is called the throne or Kingdom of the Lord. Hence, when David sat on his throne, he was biblicaly sitting on the throne of God.
Of all my sons (for the LORD has given me many sons), He has chosen my son Solomon to sit on the throne of the kingdom of the LORD over Israel
1 Chronicles 28:5
All the promises that seem to be of a physical kingdom, then, can be otherwise interpreted to mean something else. All the promises that many would attribute to a future physical kingdom of God in Israel, as well, could be otherwise interpreted to accommodate.
A Heavenly Kingdom
All this to indicate that, from a study of what the Scriptures say about the Kingdom of God, it indicates that it is a Spiritual, and not an earthly Kingdom.
As Jesus put it,
No one can see the Kingdom of Heaven unless He is born again.
The converse of this would also be true. If it can be seen by a non-believer, it is not the Kingdom of God.
There is no doubt that when Jesus was on the Earth, He said the time was then (Mark 1:15), and that the Kingdom He brought was Spiritual then (John 18:36). From the preaching of Paul, we read that he was still preaching the Kingdom in the last 2 verses of the book of Acts (Acts 28:30-31), as he was throughout his epistles. There is no valid argument that says the Kingdom was offered to Israel and then withdrawn.
When attempting to answer the question of what the Kingdom was, his response was, by interpretation, faith like a mustard seed and the Holy Spirit in the heart of the believer (Luke 13:18-21, above).
When answering contentions, Paul indicated that the Kingdom of God was not a matter of talk, but of power (1 Corinthians 4:20), indicating that, at least to some degree, his understanding of the Kingdom of God had to do with the miraculous demonstrations through his life.
As to the answer of whether the Kingdom could be "both" physical and spiritual, we can simply say that there is neither evidence of it in Scripture, nor rationale for it to be so.
Thus, the end of the Long answer to the first part of the question is...
The Rock is the invisible, spiritual Kingdom of God which Jesus brought and announced at His First Advent.
You asked... As if the answer isn't long enough. When does the rock crush the statue.
In my reading of Daniel, several possibilities stand out. Was it at the cross? Was it at Pentecost? Was it 70 AD?
I, personally, would actually place it either at the conversion of the Roman Emperor, Constantine, or at the final dissolution of the Roman Empire, perhaps as represented with its last emperor in 478 AD.
Notice that between the four materials of the statue, there was physical conflict (war), and while one empire appeared to "replace" the previous one, in the eyes of the vision (or, of God), all four kingdoms remained until the end. There is reason to suppose, then, that the final removal of all four by the rock is not outward warfare, but something else, entirely.
In the vision, first the rock appeared, cut out without hands, and then, presumably, it fell or traveled towards the statue, and struck the statue on the toes. If one looks at the change in governmental structure that occurred, the first Roman rule in the Empire was the Principate, but this was lost in the "Crisis of the Third Century", and was replaced by the Dominate. If this is the transition between the iron legs and the iron/clay toes, towards 285 AD, then the conversion of Constantine, certainly could have been the blow, if one considers the Biblical pattern of the King representing the entire empire to some degree or another. This could make the time frame of Constantine and the 313 AD legalization of Christianity a good match.
This allows for the cutting out of the stone, it falling (over a period of some time), and then crushing the statue at the time one would expect, when Rome disappeared. Rome declined after this, with the last emperor officially in 478 AD, and eventually, as the YLT of Daniel 2:35 read, they were "broken small together", and "carried them away hath the wind, and no place hath been found for them". Indicating, there were still governments, and fragments of these, but they could no longer dominate the world.
So, The Kingdom of God (that Jesus Brought in the First Century), crushing the statue probably in 313 AD, no later than 478 AD.