"Creationism [or maybe 'originism'] is a more general theory of existence including matters other than life."
No, creationism is not a theory of anything - in the sense of scientific theory. It is a religious precept, taken on faith. It requires a God who is a priori assumed to exist in order to explain the origin of the universe and everything in it.
"Science, self-limited by its own techniques, has to 'live' with things it cannot explain."
Yep, but that doesn't invalidate the fact that science has managed to explain a great deal, including the physical concepts that allow us to communicate with each other electronically via the internet. Science is a process of acquiring understanding piece by piece, and it has served our species well over the last 400 years.
Let science be science, and religion be religion. Let's not try to mix them up - especially not in science classes.
That right and it also true that anything that science can't explain is not science and anything that science can't explain should not be in a science class.
Whether science or not people do observe stars, sun, rocks, trees, gravity, day night, seasons, comets, etc. and wonder how they came to exist. When people think about origins they do believe it is more likely that they were 'created' rather than 'evolved'. Occam's Razor if you will.