To expand upon @PRP_53's reply......even if you had a copy of the Catalina installer, you would not be able to create a bootable USB installer on a Mac that doesn't support Catalina. It is definitely very frustrating, but Apple only really cares about supporting the most recent version of macOS...everything else are token gestures.
Have you tried booting into Internet Recovery Mode using Command + Option + R to attempt to access the most recent version of the online installer that is compatible with that older Mac? Unfortunately some Macs may only boot to the online installer for the older version of macOS which originally shipped on the Mac from the factory. This would be Ok as well if it works (some older online installers don't always work correct.....token gestures after all) because you could then upgrade to a later version of macOS (may require several more steps & upgrades).
It would really help to know the exact model of this "broken" Mac so that we can figure out exactly which versions of macOS are compatible with it. That would allow us to tell you generally which Macs could be used to create a bootable macOS USB installer and which versions of macOS they could download & create.
You can get the exact model by entering the system serial number on the check coverage page here (please don't post the serial number on this forum since it is considered personal information):
Check Your Service and Support Coverage - Apple Support
For example, to create a bootable macOS 10.15 Catalina USB installer you generally need a Mac model 2012 to mid-2020. You can confirm a particular Mac is compatible with a specific OS by using the information in the following article since the model years I mentioned are just close generalizations and there may be some exceptions:
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
For
- macOS 10.13 -- a model Late-2009 to mid-2018
- macOS 10.11 -- a model 2007 to 2015
As you can see there may be quite a few options for you. If you don't have access to another Mac that is compatible with an OS that the "broken" Mac supports, then you can check with other family members, friends, co-workers, or perhaps your school/employer's IT department. Or you can check with a local Apple Authorized Service Provider to see if they could assist you with accessing Internet Recovery Mode or in creating a bootable macOS USB installer.
