Head engaged at 37 weeks?

F

I'm 37+3 and my midwife said today that baby's head is 3/5ths engaged. This is my second baby and I've read second and subsequent babies normally don't engage until labour.. Do you think this means labour is close? (My daughter was born at this exact point!) How long after your second baby started to engage did you go into labour? 🤞🏼🤞🏼