I wondered the same thing & someone told me that I would know when the baby was starting to engage. They were right!!
You'll notice that your belly is lower & because of this you'll also be able to take a deep breath (finally!!). There will also be more pressure on the bladder, so more frequent trips to the loo. You will also have aches in your lower back, legs & groin area & will find it harder to move around.
My midwife told me that babies can engage as much as 4 weeks before the due date & still be late!! My baby started to engage around 35 weeks too.
Sounds like things have definitely started to get moving for you!!