The God that atheists and agnostics typically don't believe in (i.e. a supernatural being as described in various major religions) is one option for the Higher Power referred to in the Steps.
The AA programme broadens the notion to cover not just a traditional God (or Gods) but a Higher Power or a Power Greater Than Ourselves.
Firstly, the self that this Higher Power has to be greater than is the marshalled forces of an individual's own intellect and willpower.
Is there a power greater than this?
If you've ever experienced learning something from others and finding the willingness, strength, and wherewithal to achieve something because you're acting in concert with others, something you could not have done alone, then you've accessed a power greater than yourself.
If you've ever been encouraged when disheartened; if you've ever been shown a better way to look at a situation; if you've ever accessed inner resources you did not know you had because of contact with others, with nature, with music, with literature, with art; if any of these are true, you've accessed a power greater than the 'self' of 'intellect + willpower'.
There's nothing wrong with intellect and willpower, indeed they are both necessary for sobriety. We've got to think, and we need some willpower. But alcoholics by definition find this insufficient to guarantee sobriety.
Yet millions of alcoholics, previously unable to stop, are sober. The gap between what we could do individually and what we're able to do collectively: that's a manifestation of a Higher Power.
Doesn't need to be religious; doesn't need to be supernatural.
Prayer is a way of addressing that Power. Even without a notion of a supernatural being with ears literally listening to you, it still works, oddly, to focus the mind and establish the right relationship with that Power. The smart money is interested in results not dogma.
Same with meditation. It works. Isn't that what we want?
So, if you're willing to believe that there are forces in the universe that can affect an individual beneficially, you're willing to believe in a Power Greater Than Yourself.