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You'll have to be more precise on the definition of God. There are quite a lot of them.
The existence of an abstract concept is provable by thinking of it. If there exists an idea that you call God, then a God exists. However, that proves nothing about its properties beyond its mere existence as an idea, including whether it pertains to any real thing. Likewise, all attributes you ascribe to that idea become part of the idea, but do not automatically prove anything about reality.
Thus, the question whether there is an idea called God is trivially answered by asking it at all, but has little bearing on anything at all.
What makes ideas useful is that they group properties, and what makes them real is that there exists an actual thing having all those properties.
Thus, the question whether a real thing exists depends on the properties of that thing, so let's tackle one:
Do I believe that there can be an omnipotent entity? No. The typical argument here is "Can God create a rock so heavy, They cannot lift it anymore?" Either answer contradicts the premise of omnipotence, unless that entity can create logical contradictions, in which case all argument and reasoning is moot anyway.
In particular, do I believe that some variation of the Abrahamic God exists? No, or at least none of those I'm aware of. That doesn't mean I'm not open to being shown otherwise.
However, the idea of an omnipotent, omniscient and all-loving God runs decidedly counter to the existence of suffering, even if we ignore (or exclude) the contradiction about omnipotence.