You are describing an ideal scenario of two perfectly flat surfaces.
I have seen in real life with a basically perfectly polished flat granite stone on a perfectly polished granite table. With the stone on the table, you could not to the death of you push it down to touch. It would always hover slightly above the table without contact. It thus experienced a friction as low as I have ever seen - basically zero friction, or at only some miniscule fluid friction with the air - and would slide smoothly when pushed gently with a constant speed without slowing down. In fact, a corner of the stone was broken of from one evening when they had closed down the lab and left the stone on the table - it looked stationary but actually was slightly moving. And after several hours, it fell off the table. There was no friction to stop it.
The reason for the hovering is that the air in the gab between the two surface has nowhere to escape to. A moving air particle in the gab would leave behind a vacuum that immediately would suck in the neighbour air particle, thus never allowing for the air to disappear and for the surfaces to get any closer.
This works as long as the established vacuum is stronger than some treshold value of pressure on the surfaces. When you overcome this, then the air will finally be squeezed out and the surface will meet. And they will never be separated again, since that would create yet again a vacuum holding them strongly together.