Generally speaking, students break into it via ISV (independent software vendors, the big ones in this space are IBM and Broadcom but there are many others) apprenticeship and training programs, before getting deployed on site (or staying at the software vendor if you are very good or they have need of somebody junior for a position) or other paid Apprenticeship type positions, where you spend about a year studying usually paid before getting your first "real job" under a mentor.

The extreme experience requirements are generally exaggerations. They only happen to exist because there are people who really do have those many years in this field. But I've gotten jobs (I'm a systems programmer, many hats style, z/OS and Linux and C and JCL and Shell and REXX etc) and I've gotten jobs before from these sorts of excessive experience postings before despite me being fairly new to the field (just reaching senior level, about 5 years experience in my subdiscipline, which is systems programming, as opposed to applications programming or security, two other primary specializations for people with CS degrees, there is also operations and IT work available for mainframes but probably the pay rate would be of no interest to somebody on HackerNews).

Your Linux and Unix experience will carry over. Experience programming in shell and C and just general systems admin experience would carry over (to my type of position). But you likely won't match your current salary without extensive experience on a particular area in the mainframe ecosystem, you would be coming in at a junior to mid level. There are decades worth of things to learn when it comes to mainframes, and more and more of it is handleable via z/OS Unix these days and languages like Python and Node are making their debuts on the platform....but a lot still requires very deep and very specific systems knowledge about these very cool operating systems. The good news is that the IBM documentation is actually really solid in comparison to your typical Linux distro, the bad news is you really do need to read it because this is NOT as user friendly as Linux, and that's being charitable to the mainframes because I genuinely love my job working on them.