I imagine that it must have been before Pyrrhus of Epirus attacked because they’d been gobbling up lands way before than that. I remember reading a book by Anthony Everitt wherein he says that at some relatively early period the Greeks were jealous that the Romans could achieve through consensus and compromise in their own society what the Greeks themselves could barely do through internecine war and strife, and I seem to remember this being in either the late 4th or very early 3rd centuries BC. They had long thought of them as part of the Barbarian rabble, but some also noted that they governed with a constitution with complex laws and a series of checks on the power in their Republican government. So when did they go from a Western backwater to a group worthy of attention?
Greek scholars had more or less vaguely aware of the Romans for some time before they tangled with Pyrrhus. But it was only after they defeated Pyrrhus that the Romans really began to be taken seriously by the Hellenistic world.
As you suggest, the late fourth century BCE was something of a watershed in Greek scholarship on Rome. The Romans had been mentioned sporadically before this - a century earlier, the Greek historians Hellanicus and Damastes had connected Rome with the Trojan hero Aeneas - but it was only in the late fourth century that Greek historians and philosophers begin to show real interest in (if not yet real knowledge of) Rome. The Gallic sack of Rome (c. 390 BC) was the first event in Roman history to stir interest among the Greeks. As Plutarch notes in his Life of Camillus:
"It would seem that some vague tidings of the calamity and capture of the city made their way at once to Greece. For Heracleides Ponticus, who lived not long after that time, in his treatise "On the soul," says that out of the West a story prevailed, how an army of Hyperboreans had come from afar and captured a Greek city called Rome, situated somewhere on the shores of the Great Sea.....Aristotle the philosopher clearly had accurate tidings of the capture of the city by the Gauls, and yet he says that its savior was Lucius, although the forename of Camillus was not Lucius, but Marcus..." (22.2-3)
Clearly, some Greeks were beginning to be intrigued by Rome in the fourth century BCE. Just as clearly, they still knew rather little about the city. It is unlikely that the Roman constitution was one of the 170 that Aristotle and his students analyzed during research for the Politics. Polybius, however, would interpret the Roman constitution along Aristotelian lines in the second century BCE - and that, I would guess, is what you're remembering from Everitt.
The sensationalist Greek polymath Duris of Samos mentioned the great Roman victory at Sentinum (295) in his lost Histories. Around the same time, Aristotle's student Theophrastus apparently discussed Roman history and customs, and the historian Hieronymus wrote about Rome's early history. Not until the defeat of Pyrrhus twenty years later, however, did the origins and customs of the Romans become a genuinely hot topic in Greek historiography, inaugurating a tradition that would culminate in the works of Polybius, Dionysius of Halicarnassus, and Plutarch.