I imagine their lives were much more physically demanding than today so they’d be naturally more fit than us. But for example the military did they train physically other than tactics and combat?
Speaking only for the ancient Greeks: if their warriors trained at all, it was only in general fitness. They never trained tactics or combat. They thought a warrior should have stamina, agility and endurance, and that would see him through. I wrote a short post about Greek physical exercise here and in more detail about exercising for war here and here and about Spartan training here.