Sorry to be late to this discussion, but I think the explanation for the starting vortex is simple and the same as for the trailing vortices: conservation of mass.
Conservation of momentum says the lift is due to the wing imparting a velocity to the fluid that is at right angles to the free stream. Ideally, that wake wash velocity is uniform over the span of the wing. The wing has a finite span, so the deflected wake also has a finite span. If the lift has been produced for a finite time, then the wake also has a finite length.
It really is the same flow pattern one sees when a canoe paddle is drawn through the water. If you view the wing in the steamwise direction, you see the same flow pattern. The paddle displaces a slug of fluid sideways, and a strong vortex forms that wraps around the paddle, running down one edge, across the bottom, and back up the opposite edge. It is very clear the vortex forms because the water displaced on the front side has to go somewhere, and the water fills in what would otherwise be a void on the backside of the paddle. That's conservation of mass - the fluid is a continuum, and for the flows we're talking about it's negligently compressible. That means the entire flow has to form a consistent picture.
The starting vortex is the equivalent of the vortex at the bottom of the canoe paddle. Since the displaced fluid has a finite length, there must be a displacement and a replacement at the downstream end of the displaced fluid. It's not different from the displacement and replacement that occurs along the edges of the wake, forming the trailing vortices. And for that matter, the flow pattern must include the bound vortex at the upstream end of the displaced fluid. Conservation of mass is why vortices that are entirely in the fluid must form closed rings.
You don't need CFD or fancy math. Just observe the humble canoe paddle.