This question is somewhat inadequate because it uses the word “Science” in an unqualified way. This word means vastly different things depending on whether we are talking about repeatable experiments about the present working of nature, or whether we are talking about claims in the past which are not repeatable (i.e. forensics).
I wrote an essay on this for the Journal of Creation, but it’s not yet available for free online and requires a subscription.
Price, P., Examining the usage and scope of historical science—a response to Dr Carol Cleland and a defence of terminology, Journal of Creation 33 (2):121–127, 2019.
Cleland jumps on the bandwagon of attacking the criterion of falsifiability, but she does it based upon a mischaracterization of Popper’s position.
In its most basic formulation, falsification is nothing more than pure logic. If you state “Only A”, and then I present “Not A”, then I have proven you wrong. Without this basic understanding of logic, there is no way to do any science at all.
Historical science by nature is not subject to falsification (something with which Dr Cleland would agree), and that makes it fundamentally less trustworthy than operational science because of the “asymmetry of overdetermination” as Cleland puts it. With any given set of present-day clues, any number of possible sets of past circumstances could suffice to explain it.