When the thermostat finally opens, the water has a second alternative path through the radiator and back to the pump inlet. Most of the pump discharge water will either recirculate or go directly through the radiator. Relatively little will circulate through the engine. The engine is not sufficiently cooled and quickly over-heats. That little diverter disk is vital.
Water flows FROM the lower radiator hose TO the pump.
Not the other way around. Just to make things more complex, there's also the route through the heater. So the engine warms up quickly, and when it gets to the critical temperature of the thermostat, this opens and allows water to flow to the rad. From ambient air temperature to say 80 deg C in a minute or less. The water flows through the rad, losing heat to the cool air, and cooler water goes back to the engine.