Induction at 37 weeks

Hi everyone, is it a thing to ask your doctor for an early induction? I am currently 36-2 and want to get induced next week as my baby is already weighing 8lbs 😩 I do not want to get a c-section if the baby keeps growing. Doctor told me that I will get induced at 39 weeks but I feel he will be around 10lbs by then. I do have GD. I had 3 previous pregnancies and they were all vaginal and no complications but never been induced. Pic of baby boy 🥹❤️