There are open-source projects that attempt to do emulation of some of the larger mainframe systems (S/370, ESA/390, z) like [0] but you have a number of things working against you in that. You are more than likely not to find any newer version of, say, z/OS to run. Couple that with the fact that most mainframe programs deployed at FIs like core banking are so heavily customized commercial packages to fit an individual institution's needs, Hogan and similar [1], that they might as well be bespoke, internally developed systems. You may be able to get away with learning the basics of CICS [2] but it would be a struggle, not near as easy as fetching a linux distro ISO.

That said, I personally think that the Z architecture is completely bonkers and I would love the opportunity, like you, to learn it more in depth. My info above comes second-hand from what I've been able to piece together in my own searches.

[0] http://www.hercules-390.eu/ [1] https://www.luxoft.com/banking/core-banking/ [2] https://en.wikipedia.org/wiki/CICS , https://www.redbooks.ibm.com/abstracts/sg247952.html?Open