Well...could happen now. Mightn't happen for weeks. I know that's no help but first babies often engage quite early.

That said, I was told the exact same thing at my 36 week appointment with DD. Head fixed and engaged. OB said "I don't like to promise people their babies are coming a bit early...but this baby is going to come very soon. Hope you've got your bags packed".
Went into labour that night