We trace the evolution of the edge-on spiral galaxy NGC 3501, making use of its stellar populations extracted from deep integral-field spectroscopy MUSE observations. We present stellar kinematic and population maps, as well as the star formation history, of the south-western half of the galaxy. The derived maps of the stellar line-of-sight velocity and velocity dispersion are quite regular, show disc-like rotation, and no other structural component of the galaxy. However, maps of the stellar populations exhibit structures in the mass-weighted and light-weighted age, total metallicity, and [Mg/Fe] abundance. These maps indicate that NGC 3501 is a young galaxy, consisting mostly of stars with ages between 2 and 8 Gyr. Also, they show a thicker more extended structure that is metal-poor and α-rich, and another inner metal-rich and α-poor one with smaller radial extension. While previous studies revealed that NGC 3501 shows only one morphological disc component in its vertical structure, we divided the galaxy into two regions: an inner metal-rich mid-plane and a metal-poor thicker envelope. Comparing the star formation history of the inner thinner metal-rich disc and the thicker metal-poor disc, we see that the metal-rich component evolved more steadily, while the metal-poor one experienced several bursts of star formation. We propose this spiral galaxy is being observed in an early evolutionary phase, with a thicker disc already in place and an inner thin disc in an early formation stage. So we are probably witnessing the birth of a future massive thin disc, continuously growing embedded in a preexisting thicker disc.