“Scientific proof” isn't a thing. Empirical falsification of a hypotheses is, and it is absolutely available for the subject matter of economics (as conventionally understood; Austrian-school ‘economics’ overtly is a system of working out the implementation of deontological principles and is thus more a branch of moral philosophy than of social science, but that's an exception.)

It's true that a lot of the work done on economics is or builds on speculation beyond the present practical capacity of reliable testing due to complexity, but that's not uncommon (even if the ratio may usually be lower) in other scientific disciplines.

Lay (and particularly government) people frequently fail to understand the status of various economic ideas and treat speculation on shaky foundations of simplified models taken outside of their area of utility as approximations as truth, but that is also not uncommon in other scientific domains, though the practical consequences of it in economics may be more pronounced.

> but that doesn't make it not a science.

Not being a domain in which hypotheses are subject to empirical falsification (the closest thing there is to “scientific proof” in any domain) would, indeed, make it not a science.