It doesnt necessarily start out of the blue. Theres a build up. Its not bam youre right at 10cm with full blown contractions. And yes most first time mothers go past their due date by at least a week unless they are induced.
No labor starts all of sudden without any signs. With my son i was 37 weeks when i was having some nonpainful contractions my belly was getting hard i went in the hospital thinking i was getting sent home and i was at 4cm and had him that day. With my daughter there was absolutely no signs when my water broke at 39 weeks.. Dont worry, baby will come when he or she is ready :) good luck