"This version of AirPort Utility requires this Airport Extreme use firmware version 7.3.1 or later.?
Kind of a classic Catch 22.
The AirPort Extreme needs to have more up to date firmware installed......but....the version of AirPort Utility that you have will not allow you to install that firmware, and Apple will not allow you install an older version of AirPort Utility on your Mac.
If you have a PC that has AirPort Utility for Windows 5.6.1 installed on the device, you might be able to use the PC to update the firmware on the AirPort Extreme to a newer version that AirPort Utility on your Mac would recognize.......IF.......Apple still offers really old 14+ year old firmware.
The only way to know if this might work is to give it a try.
I don't have a PC or an older AirPort here to test, so another user will need to try to help on this one. Won't be easy, since Apple has classified the 1st Gen AirPort Extreme as "Obsolete" for a number of years.
Apple won't help, even if you are willing to pay them the standard $85-90 for support.
Frankly, I would not spend much time on this, since you can find much more up to date AirPorts on eBay for $25-50 that will work with your Mac.