TuneCore can technically never guarantee a release date as each store takes a different amount of time to process, however if you are looking to set a specific release date, all you need to do is set the “digital sales start date” on the album creation page to your desired release date. The stores will not make your release live in their store until the date you specified.*
If you want your release to go live in all stores at the same time, choose a date at least 4 weeks out. This should give stores enough time to complete their review.
*IMPORTANT: Amazon Music & 7digital both make preview clips of your song(s) available BEFORE your digital sales start date, as soon as 3-7 business days after distribution for Amazon Music and 7-10 days for 7digital. The release won't be available to buy until your release date, but if you're uncomfortable with having preview clips available before that date, please do not choose Amazon Music or 7digital as a store for distribution until after or right before your release date.
You can contact us from the email registered to your TuneCore account a few days before your digital release date and request to add Amazon Music as a store.