Is it possible that Daniel's fourth beast is not the Roman empire, but rather that the third beast is?

Daniel 7:3 And four great beasts came up from the sea, diverse one from another.

 4 The first was like a lion, and had eagle’s wings: I beheld till the wings thereof were plucked, and it was lifted up from the earth, and made stand upon the feet as a man, and a man’s heart was given to it.

 5 And behold another beast, a second, like to a bear, and it raised up itself on one side, and it had three ribs in the mouth of it between the teeth of it: and they said thus unto it, Arise, devour much flesh.

 6 After this I beheld, and lo another, like a leopard, which had upon the back of it four wings of a fowl; the beast had also four heads; and dominion was given to it.

 7 After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns.

I was always told, and always read, that the four beasts in Daniel 7 line up with the four metals of the image of Daniel 2.

That image has been historically shown to be Babylon, Media/Persia, Greece, and Rome.

Nebuchadnezzar was even told that he was the head of gold.

However, isn't it possible that the first beast in Daniel 7 is not Babylon?

Doesn't the chapter start out telling us that this at the end of the Babylon empire?

Daniel 7:1 In the first year of Belshazzar king of Babylon Daniel had a dream and visions of his head upon his bed: then he wrote the dream, and told the sum of the matters.

This is in the first year of Babylon's final king, Belshazzar.

Daniel had another vision in Belshazzar's third year:

Daniel 8:1 In the third year of the reign of king Belshazzar a vision appeared unto me, even unto me Daniel, after that which appeared unto me at the first.

The next thing described is Belshazzar's feast in chapter 5, where he saw the hand writing on the wall.

That chapter ended with:

Daniel 5:30 In that night was Belshazzar the king of the Chaldeans slain.

 31 And Darius the Median took the kingdom, being about threescore and two years old.

So, in chapter 7, in the first year of Babylon's last king, Daniel was told about the beasts:

Daniel 7:15 I Daniel was grieved in my spirit in the midst of my body, and the visions of my head troubled me.

 16 I came near unto one of them that stood by, and asked him the truth of all this. So he told me, and made me know the interpretation of the things.

 17 These great beasts, which are four, are four kings, which shall arise out of the earth.

Daniel was told that the four beasts are four kings which shall arise, the word "shall" showing something yet future.

Belshazzar, the last king of Babylon, was already reigning when Daniel had the vision.

There were no more kings of the Babylonian empire to arise after Belshazzar, he was the last.

The next king to arise would be of the Media/Persian empire.

Therefore the first beast would be Media/Persia, not Babylon, correct?

Then, wouldn't the second beast be Greece?

So, then the third beast, and not the fourth beast, would be the Roman empire, correct?

So, is the fourth beast an end-times beast?

Anyway, that is what I have thought.

Then there is also a different teaching, going around, that the four beasts are all end-times beasts.

They say that the beasts arise, as described, one after the other, but at the end of the age.

They also say that all four are all still there at the time of second advent, but only the fourth beast is destroyed.

That the first three are allowed to live, but without the dominion that they had.

Daniel 7:9 I beheld till the thrones were cast down, and the Ancient of days did sit, whose garment was white as snow, and the hair of his head like the pure wool: his throne was like the fiery flame, and his wheels as burning fire.

 10 A fiery stream issued and came forth from before him: thousand thousands ministered unto him, and ten thousand times ten thousand stood before him: the judgment was set, and the books were opened.

 11 I beheld then because of the voice of the great words which the horn spake: I beheld even till the beast was slain, and his body destroyed, and given to the burning flame.

 12 As concerning the rest of the beasts, they had their dominion taken away: yet their lives were prolonged for a season and time.

 13 I saw in the night visions, and, behold, one like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him.

So, are either of these two considerations possible, or are they both false?