Did you try to equip your soldiers with their starting gear? Don’t switch weapons, don’t change armour on them, don’t take anything new. Then if you would be able to run alien base attack you can try to check what inventory change cause the problem.
Backup save game and start new game, then wait for alien base to emerge (or build radar at the start and go for that alien base) if this works then it means that previous save can be corrupted.
I uninstalled and reinstalled the game. Started fresh. I had to play one Salvage mission to get resources, then I tried an alien base. I kept everything as standard as it came. No gear switching, nothing.
Still the AB missions wont load and freeze during load.
That is unexpected. Looks like something in alien base causes drivers to crash. But there is one more thing. Do you have automatic size of system page file? Or it is set manually? Try to increase that size to at least 8GB.