The Milky Way serves as a template for understanding the formation and evolution of late-type massive disk galaxies since we can obtain detailed chemical and kinematic information for large samples of individual stars. However, the early formation of the disk and the dichotomy between the chemically thick and thin disks remain under intense debate. Some mechanisms have been proposed to explain the formation of this dichotomy, such as the injection of metal-poor gas by a gas-rich merger such as Gaia-Sausage Enceladus (GSE), or by cosmic gas filaments, radial migration, and the presence of star-forming clumps at high redshift (z > 2). In this work, we combine astrometric data from the Gaia mission, chemical abundances from APOGEE and LAMOST spectroscopic surveys, and StarHorse ages to study the early stage of chemical dichotomy in the Milky Way disk. The Bayesian isochrone-fitting code StarHorse can estimate ages for thousands of stars in the solar neighborhood, being most reliable for main-sequence turnoff and subgiants, computing distances and extinction simultaneously. From these samples, we show that (i) there is an old thin disk population (>11 Gyr) that indicates a period of coformation between the thick and thin disks of the Milky Way before the GSE merger, i.e., the Galaxy itself could initiate the formation of a low-α disk without the need for a gas-rich merger, and (ii) this merger would have been important to stop the formation of stars in the thick disk.