Let's define some terms.
'God' is a short-hand word for the 'Higher Power'. Discard all religious definitions and past conceptions. For AA's purposes, 'God' and 'Higher Power' are synonymous.
What is a 'Higher Power'?
Well, firstly, 'higher' than what?
Alcoholics, within AA's definition, are people who cannot refrain from destructive drinking when applying the full force of their intellect and willpower. They lack the ability, i.e. power, to do so.
If such people are now sober, consistently, and often permanently, they have acquired power they previously lacked. That power is 'higher' in the sense that it is 'greater' than the full force of their intellect and willpower.
A 'Higher Power' therefore exists. To deny that a 'Higher Power' exists (in the meaning indicated above) is to assert (a) that these people are not in fact sober or (b) that these people, previously, were simply not trying hard enough or were not thinking it through properly. Neither assertion holds consistently true.
Since 'God', within AA's terms, is synonymous with 'Higher Power', 'God' certainly exists.
To be atheist or agnostic, within the terms defined above, is to be confused or in denial about the evidence before your eyes:
There have been millions of people who lacked the power to stay sober and live to good account ... but these have now accessed that power.