For flow to exist there has to be a difference in pressure in the system between inlet and outlet of the pump....
Doesn't matter how it is created or the type of pump. It's all about pump induced pressure at the inlet and outlet being different, lower at inlet than the outlet means we can assign one of them as an outlet, and expect a flow OUT. A flow that occurs regardless of a low or high ambient pressure across the whole system, its about a difference.
Then the coolant is biased to flow in the correct direction.
If it flows, and there are restrictions to the flow between block and head or from head through thermostat, you will have some pressure in the system that can be recognised as being generated by the pump and not the heat energy.
we also need hot coolant to travel down the radiator, hot stuff rises, hot air rises, hot fluid rises, convection is a thing. So there has to be a pressure difference between inlet and outlet of the radiator in order to force the hot coolant down to get cooling benefit of the finned tubes, we are pushing it from the top tank against its nature, in order to be cooled and sucking it down as well by the low pressure at the inlet of the pump.
its a water/coolant "pump"
to make the coolant flow faster
1) reduce restrictions ....bigger pipes bigger holes between head and block bigger thermostat housing fewer bends bigger or more pipes in the radiator
2) A more efficient pump, not necessarily a faster spinning pump, that creates a bigger pressure difference between inlet and outlet, it tries to move a bigger volume per minute
Dave