Not only that but even if you somehow prove it, no lawyer will take the case for actual damages. So the discrimination has to be so egregious that there’s a high likelihood that a jury will award punitive damages and that they will survive appeal.
The lawyer, in a civil case, should already have all of the evidence they need gathered by the HRC.
States, countries, etc. will differ of course.
I do wonder what it'd be like to have something proved and to have an administrative judge tell the company to hire you anyway... Wouldn't that be super uncomfortable?