We present the ultraviolet luminosity function and an estimate of the cosmic star formation rate density at 8 < z < 13 derived from deep NIRCam observations taken in parallel with the MIRI Deep Survey of the Hubble Ultra Deep Field (HUDF), NIRCam covering the parallel field 2. Our deep (40 hr) NIRCam observations reach an F277W magnitude of 30.8 (5σ), more than 2 mag deeper than JWST public data sets already analyzed to find high-redshift galaxies. We select a sample of 44 z > 8 galaxy candidates based on their dropout nature in the F115W and/or F150W filters, a high probability for their photometric redshifts, estimated with three different codes, being at z > 8, good fits based on χ$^{2}$ calculations, and predominant solutions compared to z < 8 alternatives. We find mild evolution in the luminosity function from z ∼ 13 to z ∼ 8, i.e., only a small increase in the average number density of ∼0.2 dex, while the faint-end slope and absolute magnitude of the knee remain approximately constant, with values α = − 2.2 ± 0.1, and M$^{*}$ = − 20.8 ± 0.2 mag. Comparing our results with the predictions of state-of-the-art galaxy evolution models, we find two main results: (1) a slower increase with time in the cosmic star formation rate density compared to a steeper rise predicted by models; (2) nearly a factor of 10 higher star formation activity concentrated in scales around 2 kpc in galaxies with stellar masses ∼10$^{8}$M$_{⊙}$ during the first 350 Myr of the universe, z ∼ 12, with models matching better the luminosity density observational estimations ∼150 Myr later, by z ∼ 9.