I'm being slightly humorous when I say this, but in the time of antiquity disease, famine, and wild animals probably took people earlier in life. So while they couldn't ctb easily, they probably didn't have to wait for death for too long (compared to many people now who live into their 80s and 90s).
Reasonably though, if they lived near bodies of water and had low SI they could drown. Or just stab themselves if they had access to a blade.