Basicly yes, but some clarification is needed here. There are not an infinite number of combinations as the structure of the amino acids will only allow so many combinations. Have this finite number of combinations attempt to happen milions and millions and millions all of times all over the earth where the primordal soup existed and bingo, you start having protein molecules. That's called science.
And, the process very obviously is not happening for an "infinite" amount of time because the primordal soup from which we came ceased to exist in that form millions of years ago.
Where did you get in my post that this suggests an explanation for "everything that exists"? That is not science.
If you're willing to grant the status of "science" to reasonable inferences based upon unobserved, unrecorded processes, then don't be surprised when certain folks who cannot produce an intelligent designer infer that one exists where organized matter presents itself, and call such inferences "science," too.