I would think that this depends on what you set the cadence to. Let's say you launch right now (7:45 p.m. on Thursday) and set the cadence to every Tuesday at 10:00 a.m., your emails would go out next week.
I'm not sure why it wouldn't run in the morning if you turned it on the night before. What is the cadence set to? Meaning, did you set it to go out every other Tuesday? Or a certain day of the month?
It's up to you, but I'd have the emails in there a few days early if possible to allow for testing, edits, revisions, etc.