You can choose to think that you have a good reason, but you're stretching things by insisting to people here that your thinking is based on logic. Your thinking is based on the preference of what you want to think -- because that's what you like to think.
You like to think of this supposed god as a "him". There is no sense in that. It's the way men designed their stories... catering to themselves.
The concept of time is based on our physical reality. There are many experiences and indications that our physical reality is not all there is -- it is just the one we order our lives by. So to create/imagine a god based on such a limited mode of perception is to serve a need within that reality... nothing more.
There could be many reasons why the experience we know of as "time" started, and none of these have to involve an almighty god. That is human imagination. And it seems quite primitive to imagine the idea of a god to answer every unknown. Do you see what that has turned into and what that does? It goes well beyond being a comfort for people. It is an imaginative creation used in all sorts of self-serving ways -- and people might even distort or lie or destroy to protect it. The god-idea stunts human beings from thinking and acting further on their own.
The 'reason for the existence of God' has nothing to do with logic. It has to do with imagination for serving oneself. That's the reason.
What we are able to 'see' of our Universe is not all there is. Our definitions serve our limited awareness. There is much beauty and compassion and love flowing throughout our limited awareness. Superimposing a god to explain that, and to imagine as the creator of our limited awareness, is ridiculous. I think it makes more sense to allow that there is much more than we are aware of and be courageously in awe of that being so, rather than further blinding ourselves with our fearful creations and not taking responsibility for ourselves.