According to the G4Preview Twitter account, T-Mobile may begin carrying the LG G4 as early as June 2.
While there have been no official carrier statements about the release date for the LG G4 so far, T-Mobile's promotion Twitter account for the device says it may be coming on June 2. T-Mobile is currently offering users the chance to win a LG G4 to test out before it becomes available to the public, and they are also on a US tour to show the device off.
When the G4Preview account was asked about the release date, they replied:
This comes from the companies promotional account, and not an official channel, so there is always the chance that this information is not correct. We have yet to see any carrier announce pricing or availability, but we hope to see that come soon.