Time and chance matters.

In terms of natural pathway you have zero chance.

But if your work puts you in close and frequent contact with the permanent direct hires, you can try to integrate yourself so well in their team and show that you can do their work as good as, if not better than them, to the point where when an opening comes up you can apply and they would be willing to seriously consider you.

If you work in some remote backend office then you wouldn't have that opportunity to even create an opportunity.