After you have purchased a vehicle in Florida you need to register and title it in your name. When you go to the FL Department of Highway Safety and Motor Vehicles (HSMV) or license agency to apply for the title and registration of the vehicle you must have proof of ownership and proof of required insurance coverage written or countersigned by a Florida agent.
The Insurance Division of the FL Department of Financial Services does not speak of a grace period of which to obtain auto insurance after purchasing a car. If you have auto insurance already and are replacing a vehicle on the current policy, generally an insurance company will cover the new vehicle for a few days but you will have to check with your specific insurance carrier to find out if this would be true for you.
If feasible, it is best to set up the policy before you pick up the car or as soon afterwards as possible. If you do not have a current insurance policy to cover a new vehicle, you can start here by getting a cheap car insurance quote.