The best description of (real) science I have heard is a response Susan Haack once gave at a talk – it is “doing one’s d***ed best to figure things out.”
When you look at how scientific breakthroughs actually occur (instead of descriptions of the ‘scientific method’ given in grade 9 textbooks, say) there are all sorts of tools and techniques, some of them contradictory.
It’s not really a method but a (constantly changing) toolbox, various conceptual or methodological tools which are useful in certain situations, others in others, and where application involves an in-flux know-how on the part of the scientist. It is, broadly speaking, just investigation, with the complexity that brings.
Distilled to two ideas, though, my guess as to the methodological core of scientific breakthroughs would be inspiration and coincidence.
Interestingly, phenomena commonly attributed to God are (divine) inspiration and (non-chance) coincidence.