SpaceX is a couple of launches from a minimum operational constellation of Starlink satellites. There are 300 version 1.0 satellite and 420 would be minimum network. There are about 40-50 version 0.9 satellites. It is not clear whether any 0.9 satellites can be part of the minimum network.
SpaceX is targeting service in the Northern U.S. and Canada in 2020 and rapidly expanding to near-global coverage of the populated world by late 2021 or 2022.