There are 2 parts:
1) You get FSD pretty much instantly when you pay or rent it. There's no need to drive a distance like 100 miles. You know that the payment is good when you go to the Autopilot menu and you can slide the grey buttons into green to get your FSD functions on. You also should see in that menu a request for FSD beta.
2) FSD beta requires a request. You need to click on that request to get it. Originally, it took a passing score in Safety Score for at least 100 miles. Later on, the passing score no longer needed. There were reports that you still needed to drive 100 miles even though no scores were needed. I heard you should not need to drive any distance at all at the current.