However, having evidence that that is the reason such that we can be confident it is that, rather than assuming it, is difficult.
You might say that it amounts to the same thing, but attributing the problem to the correct cause is important.
It's important because it means that if the correct cause is bias, it's actually bias in every potential employer somehow, but how do you know? How do you know it's not something with the applicant or the application?
Saying it's just a biased market means you don't even think of other things it could be, such as a badly presented CV or a missing key skill, or a difficult interviewing manner. Those are more likely to have every future employer reject you than something insidious. It's unlikely that every potential employer has such a large pool of candidates that bias is the thing that means you don't get a decent enough offer to even beat your current salary.
But if it is a cabal of horrible biased people, then that's illegal and should be challenged as such. It's horribly unfair, but that's probably the best course.