Better than blind skepticism is starting with epistemology, or the nature of knowledge, with a special emphasis on how knowledge is created and transmitted. Like many I've been influenced by "The Beginning of Infinity" by David Deutsch in this regard.

https://www.amazon.com/Beginning-Infinity-Explanations-Trans...

Examining one's personal epistemology is a significant task because it is the input to one's "mind set," defined in the below podcast with Dr. Alia Crum, Associate Professor of Psychology at Stanford, as "a mental frame or lens that selectively organizes and encodes information."

https://podcastnotes.org/huberman-lab/episode-56-dr-alia-cru...

With regards to The Scientific Method (and other ideas mentioned), I found some of David Deutsch's work thought-provoking. Namely, the idea that deductive reasoning is more effective than inductive when seeking new hypotheses. The Beginning of Infinity is a decent starting place [0]. Also related to some of Nassim Taleb's work.

[0] https://www.amazon.com/dp/0143121359