Solvable? Perhaps, but probably not.
But if it makes you feel any better, I have exactly the same problem.
Become a Patron of Ask Leo! and go ad-free!
The answer is in your question – you (and I) have a USB keyboard.
The process of booting your computer is handled first by the BIOS, and then by the Windows bootstrap loader. Neither of those have the drivers required for every possible hardware configuration, so they rely on a default. Sadly for you and me, USB keyboard support is not part of that default. It’s not until Windows loads that all the hardware on your system, including the USB keyboard, becomes available, and ready to use.
I believe, but I’m not certain, that newer computers may include a BIOS with more robust USB support. I kind of expect it, since USB has become such a popular standard for peripheral devices.
Even then, though, I think I’m still screwed. I happen to have a USB Bluetooth keyboard. As a result, USB support in the BIOS is not enough … I’d need it to support Bluetooth (a short-range wireless technology) as well. So depending on the specific type of USB keyboard you have, you may also be out of luck.
And yes, I do keep an old style PS2 keyboard in a drawer nearby, in case I need to do something with computer at some point before Windows XP starts up.