If you collect a vehicle in Austria it's almost certainly already got a vignette (pretty tricky for the rental company to operate an Austria-registered vehicle without one).

If you collect in your car in Germany, as I did, and drive it over the border yourself then you almost certainly won't get one (although I've ever been lucky!) so you need to purchase one (physical or digital) before (or as) you cross the border.

I can't speak for Austria, however that is exactly what it happens in Portugal and Switzerland.

In Portugal, we use digital ones (Via Verde) and they are activated at time of purchase.

In Switzerland, physical vignettes are always available on rented cars.

You can always buy a physical sticker at the gas stations near the border