The scientific method does indeed call for replicability. When it comes to those fields of study where the body of knowledge and the attending phenomena are either too small, or to grand to observe directing, one takes the extant knowledge and forms an informed model.

The model asks the question, if what we understand is true and the best explanation for the data and observations we have, all things being equal, we should expect to observe "this". Based upon mathematical and scientific principle and probability, we set up our experiment and run our model. If the data we derive falls within the acceptable range of probability and outliers and anomalies remain at a minimum, we begin to accept that our hypothesis and our model may be a plausible understanding for explaining the observed phenomenon.

That's the beginning though. Here's where the replicability comes in. We run it again and again. We offer it to the scientific peers so they can run it and see if they acquire similar results. If replicability holds up, after a reasonable period of time, and the reasonable veracity of the replication and consistency, the information becomes part of the scientific body of knowledge.

Science is dynamic by definition. This means that if technological developments allows scientists to take measurements that are more precise and accurate than previously possible, the understanding can be revised, or even rejected based upon the new evidence (eg. rejection of a flat earth, or the workings of plate tectonics). This dynamism conforms to the scientific method and process. John Dalton thought atoms were solid particles, we know know this is not true because of the veracity of experimentation and the demand for replicability.

Maybe you can just believe what you want to and the cat is both present and gone, alive and dead all at the same time. Does that bring us back to 'god did it" or just wishful thinking?

That is what Einstein thought, the randomness could be resolved. Since we have limits to resolution though it is moot.