There is simply not even close to enough material in the Universe to fill all the space up with air at sea level terrestrial conditions. Even if you took all the planets in the Solar System and the Sun itself and turned them into a sphere of air centered on where the Sun used to be, it would extend out only one seventh of the way from the Sun to Mercury (and Mercury is less than half as far from the Sun as the Earth is).
On the other hand, if you could throw away conservation of mass for a moment and just magically fill the entire Universe with air at sea level conditions...well needless to say the results would be disastrous. The Earth itself would pull nearby air down towards it, causing all humans to promptly be crushed into red goo, then a few seconds later the goo would be boiled by the rapidly rising temperatures as the gas heated up from increasing density and pressure. Furthermore, the pressure wave produced by the Earth pushing on the air in its orbit would cause that side of the Earth to heat up to extreme temperatures, probably causing rock on the surface to turn into gas before being squeezed back together by the accumulating air pressure. The Earth would start becoming a gas giant and would also fall towards the Sun. Meanwhile, the light from the Sun would push some of the nearby air away for a short time, but more air would be falling down onto it and forming a dense shell of air, the weight of which would quickly overcome the Sun's outward radiation pressure and collapse onto its surface. Within a few minutes, the Sun would be squeezed down so hard that higher elements would begin fusing in its core, setting off a series of explosive pulses over the next few hours. When these were over, the Sun would collapse into a black hole. The same thing would be happening to other stars (and, shortly afterwards, planets) throughout the Universe. The energy produced as air was compressed and heated entering these black holes would blow away some of the other air, but in an uneven pattern that would cause even more black holes to form. It might take anywhere from a few days to thousands of years, but before very long (at least in astronomical terms), the collective gravity of all this mass would crush the Universe back together and pull it into a singularity like that which existed at the moment of the Big Bang.