Your second and third sentence kind of contradict each other.

No, they do not. For example, look at Jewish and Muslim food laws. Back at 0AD (and earlier) science didn't know about microorganisms, but the population sure knew that e.g. mixing milk and meat was dangerous. Or that knackers, slaughterhouses and burial sites must be outside city limits to prevent disease spread.

Science is a method, it doesn't 'know' anything. Anyway, to say that there's no competition, but argue that one school of thought is 'ahead' implies a destination that both (and potentially others) are racing towards.

In year 0, the science did not know anything because "science" as we define it today did not exist. The scientific method was not widely practiced until 16th century (and even then it was severely limited).

And in another 2000 years people will laugh at you calling what we do today science. Sure, we invented a process we defined as the scientific method; but it's unfair to say that ancient people, philosophers, medical practitioners etc. didn't practice their own version thereof.

No, they came to the same conclusion

But to say something was ahead of something else implies a clear path. I think these are separate spheres of thought that make similar claims, the difference is that they make it on different bases.