High pressure alone at room temperature will only get you to supercritical fluid, which has continuous density changes with temperature and pressure. If you want liquid (which can phase change, aka boil), you need to drop the temperature below the critical temperature as well. Now, phase diagrams really only apply to pure gases because each element acts differently, and air is a mixture of elements. But, it’s mostly nitrogen and oxygen, and they behave relatively similarly, so we can sort of think about a phase diagram for it: https://www.google.com/search?q=phase+diagram+of+air&rlz=1CDGOYI_enUS990US993&hl=en-US&prmd=ivn&sxsrf=ALiCzsaO8of4T5UciV1cKC7Z__6KuT183g:1665391121805&source=lnms&tbm=isch&sa=X&ved=2ahUKEwj5rOixodX6AhVmkYkEHTU-B28Q_AUoAXoECAIQAQ&biw=375&bih=634&dpr=3#imgrc=hIjVH_jtZVTNLM

Anything below and to the right of the line is a gas. Anything to the left of the line is a liquid. Anything above the critical point is a supercritical fluid, which will totally fill its container like a gas and can no longer boil.