If we are considering Fraunhofer diffraction, which is what we normally do, then this is the diffraction pattern formed at infinity.
In practice we only need the distance to the screen to be large compared to whatever it is that is doing the diffracting.
If we have a slit size of order $\lambda$ or smaller then basically any distance to the screen is fine, but if the slit gets large we need to move the screen a long way back. For sufficiently large slits we'd have to put the screen miles away.
But in principle any slit of any size will give us a diffraction pattern that is a sinc(x) function if we put the screen far enough away. So a 0.6mm slit will give a diffraction pattern even though it's a thousand times bigger than the wavelength of the light.
