Why won't the cooling system fill on first startup of an LS swap?

Usually trapped air. LS thermostat sits low on the water pump, so a steam line is needed to purge trapped air; most LS swap radiators have a steam port, and adapters let universal radiators work.

Make sure the steam line runs to the radiator's steam port or an adapter on the upper hose, so air can purge through it as the system fills and warms up. See do I need to plumb the steam ports?