Was it during his life? If so, at what stage of him conquering... everything... was the title bestowed upon him? Did he come up with it himself? His close hangers-on? The general populace?
The Romans gave him that epithet. The earliest recorded instance is from around 100 years after his death in a play by the comic playwright, Plautus (254-184 BC):
Tranio:
Alexandrum magnum, atque Agathoclem, aiunt maxumas Duo res gessisse.
Most Roman discussion of Alexander centers on his military achievements and massive empire. Obvious reasons for calling someone great.