One thing I have found helpful, is to find the highest point in the cooling system and remove either a sender or some component so that I can fill until the water is at that point. That all but eliminates any possibility of trapped air.
Yes, air can and will get trapped in the cooling system and it will not move out by the pump alone. Ford 3.8 V6's and GM 2.8's of the mid 80's were the worst offenders for this. Nearly impossible to bleed the air from and even harder to fill.
There was a tool made later, that applied a vacuum to the cooling system, then allowed you to draw in the coolant through a hose, thus completely filling the system without a chance of air trapped in the water jacket.
Another method we used then, was to go to the highest point on the cooling system, and drill and tap a suitable location there, then add a small petcock to allow you to open it while filling and purge the air. Some European cars came this way from the factory. Saab and Volvo come to mind.
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