I’m not sure what exactly you’re looking for as an answer here. I’ll say that instead of looking for alternatives of science itself, we can list through the central tenets of science and then explore perspectives that counter one or more of those tenets. I’m not sure of the generally accepted list of tenets, so I’ll try coming up with what I think those are:

• observation: to understand the world around you, you need to be able to see/hear/feel it. Without this, you’re basically making up whatever you feel like (one could argue that the scientific method begins with a hypothesis followed by observations to test it, but the hypothesis itself has to be based in reality, which again requires prior observation of reality)
• logical reasoning: one you make observations, you try to make sense of them. You do this by applying logic on your observations. Alternative worldviews would say that this logical reasoning has no inherent advantage over, say, not having it, but those worldviews would be useless themselves because a) as far as we can tell, the world does follow logic; “the world around us doesn’t have to make sense, yet it does”, and b) if we were to still accept alternative worldviews that throw away logic, it would get us nowhere. Theories that disregard logic have no consistency and thus no utility whatsoever. You can say this about most (if not all) religions: one of the arguments I’ve heard a lot against atheism is that science is useless because it’s ‘incomplete’, hence God. But that essentially stops science in its tracks: saying we should throw away science and blindly accept any faith solely because science hasn’t solved everything already actively harms science from making progress, and the religions being presented as the alternatives don’t answer the same questions satisfactorily (or consistently) either.
• skepticism: this may partially overlap with the previous one. A huge part of the scientific method is to not blindly accept whatever is presented as model, or even observation, of the world around us. If an observation is objectively good, it should be possible to make basically the same observation by different people. If a model of reality is objectively good, it should match with the reality regardless of who tries to apply it. An alternative of this, like before, would be blind faithband superstition. Things like ‘miracles’ are not scientific because they cannot be (or at least have not been) repeatedly observed under controlled conditions. God as a model of reality is not scientific because it does not have much predictive power (as far as we can tell based on ‘prophecies’).

There may be more ways an alternative theory could try to counter science, but I think these points should give you an idea.