"What you are looking for was marketed and known as a "Whizzer" bike back
in the 40's and early 50's. The motor mounted in the frame just above
and slightly ahead of the pedal crank. Do a google and see what you can
find. By the way, I had two and they used a simple centrifugal clutch
with v-belt drive to the rear wheel. Should be easy to clone one."



Bicycle frames were a lot heavier back then.

And Whizzer clones are actually ridiculously expensive, but if you are
an amateur machinist and sand crab you might make patterns, pour
castings, and make one.