This Trophy is Missable
While this Trophy is technically missable, it's really not that hard to get unless you don't explore the extra shops in Okina City.
To get to Okina city in the first place, you need to have done several other things though. Following the main story, you'll eventually receive your Bike license and get to ride a scooter around town ect (specifically, June 8th-9th) During your time after school or on a Sunday on your day off, you can use the Scooter to ride around town. Simply rid it 3 times to 'Get a better feel for the place' and the 3rd time you'll end up at Okina City.
Once there, you can travel there whenever you want in your free time off, the Cafe is on the far right. Simply walk in, exchange some dialogue and 5000 yen later you'll get your first cup of coffee and the Trophy!
Note, this place is excellent for obtaining Skill cards from Persona's you have. The in game tutorial will explain how during your first cup of coffee.