We present new constraints on parameters of cosmic dawn and the epoch of reionization derived from the EDGES High-Band spectrum (90–190 MHz). The parameters are probed by evaluating global 21 cm signals generated with the recently developed Global21cm tool. This tool uses neural networks trained and tested on ~30,000 spectra produced with semi-numerical simulations that assume the standard thermal evolution of the cosmic microwave background and the intergalactic medium. From our analysis, we constrain at 68% (1) the minimum virial circular velocity of star-forming halos to V c < 19.3 km s−1, (2) the X-ray heating efficiency of early sources to f X > 0.0042, and (3) the low-energy cutoff of the X-ray spectral energy distribution to ν min < 2.3 keV. We also constrain the star formation efficiency (f *), the electron scattering optical depth (τ e), and the mean-free path of ionizing photons (R mfp). We recompute the constraints after incorporating into the analysis four estimates for the neutral hydrogen fraction from high-z quasars and galaxies, and a prior on τ e from Planck 2018. The largest impact of the external observations is on the parameters that most directly characterize reionization. Specifically, we derive the combined 68% constraints τ e < 0.063 and R mfp > 27.5 Mpc. The external observations also have a significant effect on V c due to its degeneracy with τ e, while the constraints on f *, f X, and ν min, remain primarily determined by EDGES.