When we start the distribution process it usually takes a few days, but we prefer to plan ahead to get everything in sync across all platforms. We can release fast, but prefer to keep at least 20-30 days in mind.
Apart from that we always advice to release on a Tuesday, Thursday or Friday to make sure your release gets the best exposure.
PS. Due to holidays (Christmas, Easter etc) almost all platform services take longer to handle things. So always try to plan something way before a holiday or way after.