$1As a new hire you become eligible for benefits once you receive 240 hours of pay over 3 full consecutive months, which you'll get by working 20 hours per week. Once you're eligible, Starbucks will send you a letter in the mail giving you a deadline by which you have to enroll. What matters is when you get paid, not when you work. So the hours you worked at the end of November, for instance, would count for December because that's when you'd get your paycheck.
Hypothetically, you might earn enough hours to qualify over October, November, and December. You'd be able to enroll in insurance in January and your coverage would start in February.
You can check your progress by looking at the "BEN/LOA Hours" line on your pay stubs or by calling the benefits center at 877-728-9236.