Transverse vibrations can induce the non-linear compression of a thin film of air to levitate objects, via the squeeze-film effect. This phenomenon is well captured by the Reynolds' lubrication theory; however, the same theory fails to describe this levitation when the fluid is incompressible. In this case, the computation predicts no steady-state levitation, contradicting the documented experimental evidence. In this Letter, we uncover the main source of the time-averaged pressure asymmetry in the incompressible fluid thin film, leading the levitation phenomenon to exist. Furthermore, we reveal the physical law governing the steady-state levitation height, which we confirm experimentally.