Depends on the store and if they're even hiring. Many times ads will be posted even though there are no positions available. Also with covid going on I believe most stores are on a hiring hold.
Starbucks stores get a large amount of applications and a lot of people to get through. chances if they don't get back to you within another week after that first week, I would look to apply somewhere else
More than a week
Go in and speak to them - there's often a ton of applications that get processed, so you should give them a face to put to the application - and introduce yourself so they can see how you act in person..
Within the week
Depending on their needs they would call you within a week or you might never hear from them.