Can't make an omelette in my all-clad pan because of sticking
It also happens to me sometimes, what I suggest you do is spread oil uniformly on the pan and make sure you pour the egg in the middle of the pan. If the pan has oil on all sides it does not matter if you add the vegetables first or later as topping on  the egg.

There is also a way out, pour the egg first, adjust flame of the burner to low
and add the vegetables on the egg. As the base gets hard enough that you can turn it on the pan, do it quickly and cook the vegetables attached with the half cooked omelette. Then enjoy eating the omelette...