cold engine, thermostat closed. you will have little or no pressure. Once engine reaches operating temp, you should have pressure-both from coolant expansion and water pump pressure.
*highly unlikely for a pump not to pump, but it's known to happen especially in pumps using plastic vanes.(in such a case, your engine will definitely overheat)
I would rather suggest that u inspect your radiator cap for poor sealing-that is usually the reason why your cooling system doesn't build pressure. Check also for leaks elsewhere... esp where the hoses join to the metal tubes, pipes.