Can people be non-theists before they replace the religious method with the scientific method? Authorities discourage or even forbid thinking; science requires thinking.
Based on my experience, the answer is an unequivocal 'yes!' Just as a child may rebel or run away from an abusive parent, people can renounce and repudiate without an identifiable replacement.
I personally began to doubt and eventually reject religion without substituting the scientific method. I began to smell bullshit, and felt in my core that what we'd been taught about the deity was crap, but I didn't feel a need for a surrogate or replacement.
Years later I discovered, or should I say, re-discovered the scientific method and critical thinking. Bottom line: I rejected the notion of a personal god, particularly the god that I'd been taught to worship, long before I learned of an argument against it / him /her. My rejection was at the 'gut level' ... purely emotional, if not instinctual. Only later did I bolster my decision to reject a deity with skepticism and reason.
I never was religious, and was taught at a fairly age about critical thinking, and or the Scientific method, so there was never anything to replace anything.