You can deliver a release with your release date of choice and some stores will have it live within a day or so, however we advise to leave a minimum of 2 weeks between the date of delivery and the requested release date.
Ideally you should leave 4 weeks or more, as this allows a period of time for all stores to process the release, and for it to appear across all DSPs on the date of release.
This is also the period in advance that many stores allocate their marketing to releases, so if you deliver at short notice then you will more than likely exclude the release from being considered for editorial support.