We use chemistry ([alpha/Fe] and [Fe/H]), main sequence turnoff ages, and kinematics determined from H3 Survey spectroscopy and Gaia astrometry to identify the birth of the Galactic disk. We separate in-situ and accreted stars on the basis of angular momenta and eccentricities. The sequence of high-alpha in-situ stars persists down to at least [Fe/H]=-2.5 and shows unexpected non-monotonic behavior: with increasing metallicity the population first declines in [alpha/Fe], then increases over the range -1.3<[Fe/H]<-0.7, and then declines again at higher metallicities. The number of stars in the in-situ population rapidly increases above [Fe/H]=-1. The average kinematics of these stars are hot and independent of metallicity at [Fe/H]<-1 and then become increasingly cold and disk-like at higher metallicities. The ages of the in-situ, high-alpha stars are uniformly very old (13 Gyr) at [Fe/H]<-1.3, and span a wider range (8-12 Gyr) at higher metallicities. Interpreting the chemistry with a simple chemical evolution model suggests that the non-monotonic behavior is due to a significant increase in star formation efficiency, which began 13 Gyr ago. These results support a picture in which the first 1 Gyr of the Galaxy was characterized by a "simmering phase" in which the star formation efficiency was low and the kinematics had substantial disorder with some net rotation. The disk then underwent a dramatic transformation to a "boiling phase", in which the star formation efficiency increased substantially, the kinematics became disk-like, and the number of stars formed increased tenfold. We interpret this transformation as the birth of the Galactic disk at z~4. The physical origin of this transformation is unclear and does not seem to be reproduced in current galaxy formation models.