They can cut the hole in the ice first and then get James to drive over it. The produces probably practiced it on another car before shooting the actual segment.
The hole just so happened to be fairly round and slightly smaller than the car, yet only a few meters away, the ice is seemingly a good foot deep. They just happened to have a camera perfectly lined up on it which was rolling just as it went in.
It’s all very convenient, that’s before you consider where just the right tools and logs came from to get it out.
Almost everything in TGT is scripted, some of it to a lesser extent than others but that was something which was planned well in advance.