Generally, if you want your release to go live on all major sites at the same time, you should choose a release date a minimum of 2 weeks out from the day you submit for distribution. This accommodates the processing time on CD Baby's end, and on the partner sites, and you can use those weeks to create a buzz about your upcoming release, submit for playlist consideration, etc.!
It takes CD Baby roughly one to five days to review your release. Unfortunately, we don't have a way to rush this process. Each store also needs time for their own review, and to process the data we send them after you finalize your submission:
Spotify: 2 days to 2 weeks.
iTunes: from 5-7 days to 2 weeks
Every partner site should process your music within 1-4 weeks
All of our partners do honor release dates and will not make a project available to the public until the date you select. So, if you "submit for distribution" on the first of the month and your release date is any time after the 15th of that month, you'll usually be up and running on the date you picked!