GRB 190114C is the first gamma-ray burst detected at very high energies (VHE, i.e., > 300 GeV) by the MAGIC Cherenkov telescope. The analysis of the emission detected by the Fermi satellite at lower energies, in the 10 keV–100 GeV energy range, up to ∼50 s (i.e., before the MAGIC detection) can hold valuable information. We analyze the spectral evolution of the emission of GRB 190114C as detected by the Fermi Gamma-Ray Burst Monitor (GBM) in the 10 keV–40 MeV energy range up to ∼60 s. The first 4 s of the burst feature a typical prompt emission spectrum, which can be fit by a smoothly broken power-law function with typical parameters. Starting on ∼4 s post-trigger, we find an additional nonthermal component that can be fit by a power law. This component rises and decays quickly. The 10 keV–40 MeV flux of the power-law component peaks at ∼6 s; it reaches a value of 1.7 × 10⁻⁵ erg cm⁻² s⁻¹. The time of the peak coincides with the emission peak detected by the Large Area Telescope (LAT) on board Fermi. The power-law spectral slope that we find in the GBM data is remarkably similar to that of the LAT spectrum, and the GBM+LAT spectral energy distribution seems to be consistent with a single component. This suggests that the LAT emission and the power-law component that we find in the GBM data belong to the same emission component, which we interpret as due to the afterglow of the burst. The onset time allows us to estimate that the initial jet bulk Lorentz factor Γ₀ is about 500, depending on the assumed circum-burst density.