There are 3 possibilities:

Use a single grid, e.g. 256^3, and live with the limitation it covers only the scene near the camera. Other stuff can blend with baked GI or no GI at all or whatever.

Use nested grids, e.g. 256^3 * 4, each having twice the resolution. Similar to mipmaps or terrain clip maps. The grids can move with the camera, largest one may large enough to cover the entire scene so no need to move. Larger levels could also represent only the static parts of the scene, so only the part of the volume scrolling in has to be generated per frame.

Using an Octree. In Crassins paper he uses 3x3x3 bricks which allows hardware filtering of a 2x2x2 blocks. Requires less memory but is (much) more expensive to build and trace. I don't think there is a game out that uses octree, but i would not reject the idea. Larger brick sizes could eventually make sense.

Generation on GPU: https://developer.nvidia.com/content/basics-gpu-voxelization

Nice thread with details about performance (see profiler numbers in screenshots): https://www.gamedev.net/forums/topic/696476-implement-and-understand-voxel-cone-tracing/?page=3