The keyboard is derived from notation and it’s note name conventions. And it’s all due to Gregorian chants. Western notation was invented to record Gregorian chants.
Key signatures are really based on A minor, not C major. Most Gregorian chants were in A minor, and that’s why the notes start with A. At the time there were 8 diatonic notes in A minor- A through G plus Bb. “Bb” was originally “B” and “B” was “H”. This is why “H” is used for B in some parts of Europe.
Keyboards were invented to ring bells to accompany the Gregorian chanters. The very first keyboards had no black keys, the black keys were added shortly thereafter and over the next few hundred years the keyboard layout was developed and moved from 8 “white” and 4 “blacks” to the 7 and 5 we know today. Before equal temperament took hold on some harpsichords the black keys were split into two keys like D# and Eb.
As Western notation matured over the centuries we arrived at the staff notation and key signatures we know today. The keyboard layout we know today was so well designed and redesigned to work with Western notation that it’s easy to think it was the other way around.