Typically the Hellenistic Age is defined as the years between Alexander’s death and the Battle of Actium. I humbly offer another definition. My own interpretation of Hellenistic is Greek-ish, Greek-like, Greek-esque, etc. Perhaps I am misguided in this definition, but there it is.
The Hellenistic Age should be considered begun after the Battle of Chaeronea, or alternatively at the foundation of the second League of Corinth when Philip essentially declared Hegemony over Greece. If the Macedonians were taken to be Greek-esque in and of themselves, then the rise of Pseudo-Greeks as the dominant force, and in particular a force that begins to expand, heralds the rise of the Hellenistic Age.
In my as-of-yet unwritten Master’s thesis, I endeavour to show that Philip II actually had more to do with the creation than did Alexander, whereas Alexander only incorporated the territory, which in turn made these separate kingdoms significantly larger than they could have been otherwise.
Philip’s rise over the traditional power of mainland Greece brought about a significant change in the balance of power and brought about a new epoch in history far more than did Alexander or Alexander’s death, ergo the Hellenistic Age should be dated to Philip’s ascension, not Alexander’s death. That the Hellenistic age is not taught as a cohesive period is another issue altogether.