Fill using the radiator. I would then run the engine with the heater on & cap off so you can top up as needed whilst the air exits. This should take a few minutes max during which it can help to flip the throttle.
Once happy the air is out, turn off the car. Put the cap on the rad & open the expansion tank. Fill the expansion tank to the level & close.
With both tanks closed go for a drive till the car is at temperature. Keep the heater open till you are happy it is working.
Then park up at home & let it all cool down. Then you can recheck the expansion tank & fill if needed.