Hypothetically say China and U.S. do even a tit for tat exchange and take out one of each other's satellites with an ASAT.

Given how much more we have in space these days I don't think it would take much at all to kick off Kessler Syndrome.

In the event of WWIII I think it's safe to assume that the space aspect of the war will be short lived. As it's all going to be shredded.