Indeed, the launch date is there, but it's only accurate to the day. To figure out the actual launch date+time, you need to look at the deadline and subtract the project duration, both of which can be found in this element on each page:

<span data-duration="X" data-end_time="Y" id="project_duration_data">

Wow, thanks. Was this always there, or did it come as part of the recent redesign? I remember searching the source of the previous project pages for anything resembling what should have been a launch date, and couldn't find it anywhere. Maybe at the time I was just delirious.

Not sure how long it's been there, but I feel like it's not a super-recent addition. I never really paid much attention to the launch dates.