Was bootloading from punch cards possible on System/370 machines?

Short answer: yes. In the 1970s it was standard to IPL ("initial program load" == boot) using a short deck of cards. As I recall you dropped the cards in the card reader, and brought the system up by reading the deck, which then pointed the processor to read the OS from disk. In principle it's not that different from BIOS.

It's been a while since I did that.

(Edit: typo)

I think so; there's a series on youtube that takes one through the IPL process on a virtualized (Hercules VMM) mainframe; part of the process of booting involved creating files on the emulator host that corresponded to a boot card deck (for the virtual card reader) and an OS (for the virtual tape drive), IIRC.