How much time between fall of Greece and rise of Rome?
The Roman Empire began 7 years before Alexander the Great died.
The point of Daniel's prophecy was that 4 beasts would control Judah/Jerusalem.
After Alexander the Great died, the Seleucid Empire was a Hellenistic empire ruled by the Seleucid dynasty. They were Greek kings, such as Antiochus III, who ruled over Judah/Jerusalem.
They ruled over Judah/Jerusalem until the Roman Empire ruled over Judah/Jerusalem.
Like I said, everything happened exactly how Daniel said it was going to happen in Daniel Chp 11.