Big baby!

So I had my 36 week appointment yesterday and during the ultrasound I was told he is measuring a week and a half/two weeks ahead! I’m scheduled to have a C section on May 15th which would put me at 39 w 1 day.

My doctor said there is a chance I could go into labor on my own before but she won’t be pushing up my c section date.

Have any of you experienced this with past pregnancies? Did you go into labor early? Or did you make it to your due date/c section date?