We present a sample of six F200W and three F277W dropout sources identified as 16 < z < 25 galaxy candidates using the deepest JWST/NIRCam data to date (5σ depths ∼31.5 mag at ≥2 μm), provided by the MIRI Deep Imaging Survey and the Next Generation Deep Extragalactic Exploratory Public survey. We estimate ultraviolet (UV) luminosity functions and densities at z ∼ 17 and z ∼ 25. The number density of galaxies with absolute magnitudes of ‑19 < MUV < ‑18 at z ∼ 17 (z ∼ 25) is a factor of 4 (25) smaller than at z ∼ 12; the luminosity density presents a similar evolution. Compared to state-of-the-art galaxy simulations, we find the need for an enhanced UV-photon production at z = 17–25 in MDM = 108.5‑9.5 M⊙ dark matter halos, provided by an increase in the star formation efficiency at early times and/or by intense compact starbursts with enhanced emissivity linked to strong burstiness, low or primordial gas metallicities, and/or a top-heavy initial mass function. There are a few robust theoretical predictions for the evolution of galaxies above z ∼ 20 in the literature; however, the continuing rapid drop in the halo mass function would predict a more rapid evolution than we observe if photon production efficiencies remained constant. Our z > 16 candidates present mass-weighted ages around 30 Myr, and attenuations A(V) < 0.1 mag. Their average stellar mass is M⋆ ∼ 107 M⊙, implying a stellar-to-baryon mass fraction around 10% if the emissivity increases with redshift, or significantly higher otherwise. Three candidates present very blue UV spectral slopes (β ∼ ‑3) compatible with Population III young (≲10 Myr) stars and/or high escape fractions of ionizing photons; the rest have β ∼ ‑2.5 similar to the z = 10–12 samples.