Greece was at war with pretty much everybody at some point. But in a war involving warriors who were made invincible by the gods (except for the heel)? No. With Amazons (women warriors)? Maybe; there's no reason women can't put on armor, pick up a weapon, and fight. With Centaurs? If you mistake a man on a horse for a single being... but I very much doubt that cultures that depended on horses would be that ignorant.
The story of the Trojan War involves gods - in short, supernatural beings. So no, it could not have happened exactly the way that the stories say it did. Assuming, of course, that it happened at all.
This part of the thread's argument got me interested in revisiting a documentary series I last saw 30-odd years ago: Michael Wood's
In Search of the Trojan War. It's all there on YouTube, 6 episodes.
I plan to watch this, to refresh my memory.