It's not an exact date, but Square Enix confirmed FF14 Dawntrail will launch in Summer 2024. Yoshida mentioned he'd love to get the expansion out "as early as possible" in the keynote but wants fans to remember that it's summer "generally," just in case the MMO needs a little more time to cook.
The game's history tells us delays aren't out of the question but are typically shorter waits. FF14's first three expansions all launched in June or July, while Endwalker pushed its original November date back by two weeks, where it launched on December 3, 2021.