An even simpler scenario is to remove the grandiose overcomplication of an infinitely powerful, inifinitely old, infinitely knowing, infinitely etc. being, and just say "stuff happened", since that's as empty and sweeps as much under the rug as the "God did it" waffle -- both make a simple declaration and run away from the messy details of exactly how.
For that matter, even if one insists on including a sentient creator because one hasn't the imagination to envision any other kind of possibility, Ockham's razor would favor an advanced alien from the universe next door working on his Cosmogensis 101 term project, rather than the aforementioned inifinitely infinite being. "Sufficiently powerful" is closer to the spirit of Ockham's razor than "all powerful". After all, one doesn't automatically presume divine creation for a macaroni sculpture.
Perhaps there is some truth to that in cosmology.
And perhaps there isn't.
The question for scientists then becomes "How did God do it?"
Presumes facts not in evidence. One could equally well say that the question for scientists then becomes "How did the invisible pink unicorns do it".
Modern science's outright rejection of higher power(s) is unscientific.
It would be if modern science actually engaged in "outright rejection of higher powers", but since it doesn't, you're just revealing your misunderstandings about science.
Not at all. "Modern science" is no longer simply interested in seeking the truth, but is actively engaged in propping up the philosophy of non-theistic materialism. The caterwauling of many atheistic scientists that ID (which simply proposes that life is intellegently designed, not that it all happened 6000 years ago or that no evolution has taken place) is just a back-door for creationism is one proof: If they were not actively engaged in trying to fiat out "higher powers," they would no more be threatened by ID than geologists are threatened when an archaeologist proposes that a weathered bluff shows signs of having been artificially constructed as a wall.