There are ways to get along in common life while only making distinctions between "more" and "less", although you will still probably need counting, for example the classic case of shepards making tallies. For complicated behavior, numbers will inevitably arise. For example, the earliest writing we know comes from an sumerian accounting of a barley warehouse in Uruk making beer, which counts incoming and outgoing shipments. It miiight be possible to skip this sort of step some amount by only using comparative weights or things, although I would imagine to simplify things you'd want to move to a standardised system of weights, which it seems would inevitably progress towards some being multiples of others.
At the very least, a species advanced enough to develop ways to understand things like atoms or chemical bonds will have to start making distictions between hydrogen and helium all the way to lead etc, or HO and HO2. If they didnt think about numbers before, this will require them to in some regard.