It depends a great deal on how you define "faith".
Human civilization has often tied together the concepts of 'explaining the natural world', 'explaining the birth of nations', and 'encouraging people to follow the rules of society', which we tend to lump under the broad concept of gods and the supernatural.
While the first aspect could be largely done away with in a society that somehow attained advanced science early, and the second aspect can be done away with if a nation recorded its history accurately from the very beginning, the third aspect is very difficult to pull off without either
- belief in some kind of moral code that exalts people who live according to its laws and encourages people to look down upon those who do not, or
- an authoritarian rule, often operating under a totalitarian dictator who effectively functions as a god incarnate, at least in the eyes of the people.
Atheistic societies can exist only if they substitute 'gods' with a suspiciously similar substitute that encourages society-promoting behavior, which generally relies upon faith that the system will work and people who "follow the rules" will be "rewarded" for their behavior in the end. Without this, society will devolve into anarchy. Most humans are not altruistic enough to reliably make sacrifices without the belief that they will get something in return. (A society built by a naturally altruistic eusocial species, such as intelligent ants or bees, may be different.)
While anarchistic societies based on merit and natural social encouragement/discouragement can and have existed (the first human societies were like this), they are by nature small - no bigger than the average "social circle" - since every person must be aware of every other person in the society to ensure people are contributing and reward/punish behavior appropriately. A major civilization could not develop in this state.