The core of the scientific method is to have an observer, something to observe, a mechanism for generating and evaluating predictions about future observations, and a way to either select similar future observations or generate new similar events to observe. You then observe, model, test, observe, model, test, etc., as a way of improving your predictor's performance.
The constraints are therefore extraordinarily weak, though not exactly the ones you describe. Conditions need to be temporally stable enough so that you can run your observe-model-test loop many times before the rules completely change (slow drift in rules is okay, if you know to expect it); outcomes need to be sufficiently reproducible so that there is something to predict (but broad distributions are okay). Both randomness and extreme complexity can frustrate reproducibility; the more sophisticated of an observer/modeler you are, the more complexity you'll be able to tackle.
Vastly stronger than the constraints on the rest of the world are the constraints on the observer and modeler (possibly the same entity, though there is no reason it needs to be; the observer can use a modeler-oracle). Between the pair of them they need to be able to translate events into a representation of those events, detect which differences are purely stochastic and which are regular, and devise some sort of compact representation of such things that can be used to make future predictions. This is an immense amount of computational work, and it seems unlikely that in a badly chaotic time-varying universe that such entities could exist.
So the answer is probably very close to: if you exist and have adequate capacities to attempt to follow the scientific method, you can probably use it to find out at least some things.