At 36 and a half weeks with DS1 my waters broke. At hospital, they said they would keep me in but wouldn't induce me, unless there were any signs of foetal distress or that I had contracted an infection, until 38 weeks, given that this is the last stage of the development of the baby's lungs.
I was monitored every day - my bp and the baby's heartbeat and any possible contractions/BH.
During the day before I finally went, spontaneously, into labour, the monitor was showing nothing - not even BH.
That evening, at around 10.15 I started to get niggly period pain-type pains. At 2.15 DS1 was born!
I can tell you that all hell broke loose, as no-one expected anything like this to happen. The midwives were not allowed to examine me internally for fear of creating an infection, so when one of them finally did, she clearly thought I was going to be only a few centimetres dilated. She examined me, and then had to do it again, just to check. She then kicked the brakes off the bed, called for help and rushed me (on the bed) into the labour ward as I was already 9 centimetres dilated!
So - it can happen very quickly.