the genset pic you posted above, usually have starter system, called a self. This is similar to a car.
A starter motor connected to a battery with gearing is used to start the generator. The flywheel of the generator contains a geared ring, when the starter is switched ON, the gear of the starter motor engages with the geared ring in the flywheel turning it, after the generator starts the gear arrangement in the starter motor automatically gets dis-engaged. Additionally the genset engine would have an alternator also to keep the battery charged.
The gear assembly is also called a Bendix gear, and is used in cars. The starter switch is usually spring loaded so that on releasing the contact are disconnected, thus allowing the generator to run.
To use a PIC a suitable contactor can be energised by a PIC, but there must be a feedback from the generator indicating that the generator has started, keeping the starter running persistently even after the generator has started would damage the gear assembly. Perhaps you could use the alternator terminals for this.