How did our predecessors drink before pottery was invented? You just cannot stay for all time close to a source of water, right? I suggest a kind of fruits/veggies might be a better source of water especially when you move.
Wooden buckets, waterskins and berries are indeed the solution. Indigenous people of the Great Plains and Canadian Prairies used buffalo intestines and stomach to make waterskins and travel the plains.
But eating raw... what numbers of fruit/veggies you need to cover the same amount of water?