Context. Recent high-redshift (z > 4) spatially resolved observations with the James Webb Space Telescope have shown the evolution of the star formation rate (SFR) surface density (ΣSFR) and its main sequence in the ΣSFR ‑ M* diagram (ΣSFRMS). The ΣSFRMS is already observed at cosmic morning (z ∼ 7.5). The use of ΣSFR is physically motivated because it is normalized by the area in which the star formation occurs, and this indirectly considers the gas density. The ΣSFR ‑ M* diagram has been shown to complement the widely used (specific) SFR-M*, particularly when selecting passive galaxies. Aims. We establish the ΣSFR evolution since z = 12 in the framework of the L-GALAXIES2020 semi-analytical model (SAM), and we interpret recent observations. Methods. We estimated ΣSFR(–M*) and the cosmic star formation rate density (CSFRD) for the simulated galaxy population and for the subsamples, which were divided into stellar mass bins in the given redshift. Results. The simulated ΣSFR decreases by ∼3.5 dex from z = 12 to z = 0. We show that galaxies with different stellar masses have different paths of ΣSFR evolution. We find that ΣSFRMS is already observed at z ∼ 11. The simulated ΣSFRMS agrees with the observed one at z = 0, 1, 2, 5, and 7.5 and with individual galaxies at z > 10. We show that the highest ΣSFRMS slope of 0.709 ± 0.005 is at z ∼ 3 and decreases to ∼0.085 ± 0.003 at z = 0. This is mostly driven by a rapid decrease in SFR with an additional size increase for the most massive galaxies in this redshift range. This coincides with the dominance of the most massive galaxies in the CSFRD from the SAM. Observations show the same picture, in which the ΣSFR evolutionary path depends on the stellar mass, that is, more massive galaxies have higher ΣSFR at all redshifts. Finally, using the slope and normalization evolution, we derived the simulated ΣSFRMS as a function of stellar mass and redshift.