We already believe from quantum mechanics that there are random events that have no prior cause going on all around us. Even creation ex nihil seems to be going on constantly at the smallest scale, with virtual particles popping in and out of existence governed only by laws which ensure the conservation of energy.

So, whether correct or not, our scientific understanding already posits effects without causes. Ascribing no cause to the big bang itself is then not an extra assumption, so no contorted logic is necessary to get rid of the First Causer.

And related to your description about brute facts - while perhaps unsatisfying, I believe that it is how many scientists do perceive the world. We have a set of observations and we try to come up with the simplest set of laws that describe these observations, and test their predictive power on new facts as they come along. Sometimes, we discover that our set of laws had some hidden assumption that we were not aware of, such as the surprising facts about the speed of light being constant when measured from moving vehicles leading to the realization that Newton's laws of motions only hold for small enough speeds, and the need for general relativity to accurately describe what happens at a larger scale.

Even today, we have clear, well known gaps in our scientific understanding: the standard model only applies for matter at certain energy levels; quantum mechanics only applies at certain scales and can't take into account gravitational effects; we have mathematical singularities that come up when trying to describe black holes, which are unlikely to be physically correct; and we don't know what most of the matter in the universe is made of; and I could go on.

Scientific understanding is known to be contingent and any day a new unexpected fact could be observed, toppling our understanding of the laws of physics. That is a well known and inescapable fact.

All of this is not to mention that it still seems disingenuous to call the posited First Cause 'God', bringing to mind YHWH. I would be more inclined to accept the idea that there is some kind of transcendental First Cause (though, again, I don't think that is a particularly necessary concept), but you would need many more arguments to go from that to any particular conception of god.

Also, all of this discussion relies on certain assumptions about the real world and our ability to perceive it. For example, physics is also entirely compatible with the Hindu notion of Maya, that the world is an elaborate illusion, with everything we perceive actually being like drops of water in the ocean that is God, Brahman. Not to mention that even our understanding of logic is contingent. Perhaps there is some limitation of our biological brains that prevents us from seeing some fundamental flaws in our arguments.

All in all, my point is that it is not possible to obtain true certainty beyond any possible doubt on any topic. The best we can do is choose some base assumptions we believe in, and try to see what we can understand of the world starting from those. And if you chose God as one of those base assumptions, that is perfectly legitimate, and you can get a coherent model of the world that includes it. But you can't convince someone who has chosen pure empiricismaas their base assumption of the necessity of this base assumption.