This is exactly what my rebuilt 4A did. I'd make sure the cooling system was absolutely full - park on hill to fill radiator, bleed any air out of a fitting in the heater hose - and the next time I checked the radiator would have air in it.
If it was absolutely full and I started the engine the overflow tank would fill almost immediately and there would be new air in the cooling system. I drove it to Las Vegas and back this way 4000 miles! And over mountain passes and the whole thing. If I kept it full it didn't over heat, but every time I stopped more air would get in and more coolant would come out. After several stops the temp gauge would get very high, but it never boiled.
I finally figured out that it was a bad head gasket. This was with a brand new gasket, surfaced head, retorqued head bolts and I did the work - but it was a cheapo head gasket that had come in the rebuild kit

. Get a Felpro or Toyota head gasket.
Here's how I found it: I finally realized that the air was getting into the cooling system as soon as I started the engine. So I disconnected the distributor lead and found that the air would get into it just by cranking it over. Then I pulled all the sparkplugs and cranked it over - no air! So I put in one plug and tried again, no air. Put in another plug and tried again, no air. I did get air when I put the 3rd and 4th plugs in - the leak was between the water passage and both cylinders 3 and 4.
Apparently the gasket formed a water-tight seal, even under 12 lbs pressure, but it would not hold the 170 lbs pressure of compression. The weird thing is that the gasket seemed to seal as soon as the engine warmed up a little - heat and expansion of the head caused the gasket to seal better
Replaced with a Felpro head gasket and haven't had any problems since.
Let us know what you find.