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punchit
A basic Go package to convert source to IBM 5081 (80 column) punch cards encoded by an IBM 029 keypunch (~1964).
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
If you just want the subjective experience, I recommend the Computer History Museum in California, when/if that's possible for you. About the only place where you can still load up a real deck of cards and hit RUN.
Otherwise, yes you can simulate it. There are plenty of operating systems and software from the late 50s/60s/70s that has survived. Pretty much the whole stack for a cutting edge IBM mainframe from 1974 is available. But you'll have to pick which OS and era, and then set it up, install and configure it yourself to some degree. I don't think anyone keeps an MVS system running online for public access (but I could be wrong!)
Expect many hours of reading old manuals. On the plus side, you do generally boot from a virtual punch card reader!
https://github.com/FuzzyMainframes/Awesome-Mainframes
I explored this a bit last year in a project for converting small snippets of RPG, COBOL, and FORTRAN to a punch card like format in https://github.com/barrettotte/punchit
https://www.masswerk.at/keypunch/ is a good tool for getting the basics of the punch card encoding scheme.
There's also a handful of people over at Hackaday that have made hardware for reading punch cards. Example: https://hackaday.com/2015/01/17/arduino-reads-punch-cards/