Induce labour

Hi, today is my EDD but no signs of labour. My last gynae check was 2 days ago and I was told that baby’s head is not engage yet and my cervix is still closed. The yoga ball is now my best friend. Just wondering if anyone had contractions/water bag burst without baby’s head engage and went on to have a natural delivery? I read online that it’s possible that baby head will engage during labour. Or if anyone manage to induce without baby’s head engage and was successful with natural delivery? My gynae said that if baby head is not engage then induce will fail and lead to c sec. He is willing to wait for 10 days but I’m kinda worried that overstay will be dangerous for baby. Any inputs are appreciated! Thanks!