On most types there are Engine driven pumps, these are mechanical, driven by a quil shaft from a reduction, and start working upon engine/gearbox rotation as on a start initiation, although it may not be SOP!
I would on occassion start engines with Electric pumps off, as it is a sure way of testing if the associated engines Mechanical pump is working before getting into the air.
Be sure to check your type manual or ask your engineer what is fitted to the type you operate.
N/Snort.