Install modern Linux as only OS on 2006-era 32-bit EFI Intel iMac with no CD Drive, no Admin Password, no Mac Install Disk
Standard pc linux install media will not work because it assumes bios. You need EFI install media (probably 32 bit even on 64 bit computers) and finding 32 bit EFI install media is difficult.

I think your machine may be a candidate for netbooting. The way to check is to hold down "n" during startup. If you get a globe (solid, blinking, or spinning) this will work. If not you will have to take it apart, remove the hard drive, put the hard drive in another computer, install linux, and put it back, but blessing the image becomes even more difficult.