You can drag around the 3D model on top of the footprint to position the 3D model pins in the footprint holes.
Just switch to 2D mode (2 key) and then move it around. Once the item is selected you can switch back to 3D mode and keep moving it in 3D mode. (Selecting objects in 3D mode is tricky, so I select it in 2D mode first.)
You only need to edit the numbers in the properties window for rotations, which is usually not needed if you design the 3d model flat to start with.
Note, my experience is with older Altium versions, i dont have much experience with the latest version.