A: the question makes no sense. We do not place impose criteria on a higher power. It is largely agreed there is one, not many. It is not as though there are many distinct ineffable forces we must run through an interview process (involving an application form, an in-tray test, and an interview panel).
No, there is a power. Our job is to work out whether or not to seek it. If we don't, we will be on our own. If we do not like the results we have been getting on our own, we seek the power.
We do not need to have a concept of a higher power, any more than we need to have a concept of electricity to turn on a light. We just need to flick the switch.
Rather than considering criteria, take all of the twelve steps, including telling every secret, dropping all resentment, making every amend, making arrangements to pay back every penny, sponsoring a bunch of people, and making AA the centre of your life. Do this for five years. And then come back and tell us what your concept of a higher power is, and whether or not you could have conceived of said higher power in advance.
I know I couldn't have, and it wouldn't have helped me if I could.