I have a rather strange question, let's say I can play with the temperature and atmospheric pressure conditions in a sealed room. What will I need to do to make the air's refraction coefficient greater then the glass' coefficient?
If you're talking about the index of refraction at a visible wavelength, you can't do it.
To increase the index of refraction of the air, you need to increase the density. But it's not so easy to do this indefinitely. As you increase the density (by increasing the pressure or decreasing the temperature), the air (mostly nitrogen and oxygen) will eventually liquify or solidify. The index of refraction of liquid/solid nitrogen or oxygen is less than that of glass in the visible (it's around 1.2 for liquid nitrogen).
I suppose if you kept on increasing the pressure you would compress the liquid. It requires tremendous pressures to compress liquid nitrogen. Depending on how the material properties changed as the liquid was compressed (which I don't know; I don't know if anyone has studied the properties of liquid nitrogen at thousands of atmospheres of pressure) it's likely that you could get Nair>Nglass. But it seems unlikely to me that it would be technically feasible on earth.
The refractive index is a measure that determines the reduction of the speed of light as it propagates through a homogeneous medium. More precisely, the index of refraction is the phase change per unit length, ie the wave number in the middle (k) is n times larger than the wave number in vacuum (k0).
The refractive index of air is 1.00029, while the glass is 1.52 so if you just want the air refractive index as glass is under pressure and temperature variations, you would have to increase therefore the pressure in the room to get the density $ cm ^ 2 $ is equivalent to the density of the glass. but I do not think much of it.