As you are waiting for a response, we can first note that Athens had ceased being the foremost political or military powerhouse of the Greek/Hellenistic world before the rise of Rome's power in the region. As described in earlier threads like this recent one by u/Alkibiades415 and this older one by u/Tiako, Alexander's Macedon and his successors in Asia and Egypt had become the main Hellenistic powers, and while Athens remained an (if not the) important cultural centre it was also rivalled by Alexandria, Antioch, Pergamon and others before Rome involved itself much in "eastern" affairs.

As for the second half of your question, about the rise of Rome, there are surely many factors involved and I hope you will eventually get a response from one of our experts, but for now I can link to a discussion which may provide a partial answer. Military historian and Romanist Bret Devereaux wrote a series on Roman diversity on his blog ACOUP recently, in which he argues that Roman willingness to incorporate other peoples was crucial for its rise. Really the entire series is worth reading but in the second part he explores the Roman system of allies, how they eventually were granted citizenship and how this approach differed from contemporary states like Carthage and the Hellenistic kingdoms. Again in the fifth instalment he writes about how the Roman use of other ethnic groups in its military functioned better than other states, like again Alexander's successors and also Achaemenid Persia.