Cosmogrand Zenith’s ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack without resolving. Notably, if your second spell is a creature spell and you choose the second mode for Cosmogrand Zenith’s ability, the resulting creature from that spell won’t get a +1/+1 counter.

Cosmogrand Zenith’s ability will count any spells you’ve cast this turn, which may include Cosmogrand Zenith itself. It doesn’t matter if the other spells resolved, didn’t resolve, were countered, or are still on the stack.