If SYSTEM is corrupted and you don't have a backup, then you're out of luck (with standard recovery) because we no longer have a record of what is actually even IN that database.
Even with block level recovery style tools, eg
https://www.ora600.nl/DUDE_PRIMER.pdf you would be doing something like
- extract objects definitions SYSTEM tablespace
- use those definitions to try extract data from the other datafiles
Or enlisting the help of external consultancy to try hack the SYSTEM datafile back to a reasonable state.
All of those options are a LOT of pain