P-values don't prove anything about whether an effect is real or not. They, at most, provide some degree of confidence with the presumption that the independent and dependent variables are indeed independent and dependent.

P-values should, at most, be used to direct further mechanistic studies (if possible). Only use them on their lonesome if this hasn't yet been done, or isn't possible. And if that's the case, reverify them independently (such as by doing another meta-analysis using different research).