Is it possible (not practical) to create a liquid nitrogen jet?
At best, the mechanical energy you can release by evaporating liquid nitrogen would be about its heat of vaporization, which is 5.56 kJ/mol or roughly 200 kJ/kg. (Converting this energy to useful thrust probably requires you to use the expanding nitrogen to drive a turbine that drives a fan or propeller, but that's a Simple Matter of Engineering, at least comparatively).

The chemical energy density of jet fuel is about 46 MJ/kg.

Even if we suppose the efficiency of your nitrogen engine could be a bit better than that of hydrocarbon-burning engines, this still mean that you would need to carry about a hundred times more nitrogen (by weight) than jet fuel for the same result.