I had the exact same problem. No autopilot after 100 miles, so I called Tesla and they told me it could take up to 200 miles. After passing that mark, I called again and found out that autopilot wasn't correctly configured on my Model 3. Basically I paid for it, but it didn't get activated.
I finally got on the phone with a rep who stayed escalated a ticket to the right department to get it activated. Later that day, he called back personally to tell me it should be active. Sure enough, the autopilot options where active the next time I started the car.
Bottom line, call back and ask them to double check that your car was configured correctly.