That sounds about right. First babies can engage quite early and around 36 weeks is not unusual.

Breathing easier (often combined with needing to pee a bit more because baby is putting more pressure on your bladder) is usually a sign. Some women don't notice anything at all though - I was one of them, when my DD engaged my hubby noticed it first. He kept saying for days that she had dropped but I didn't feel any different...probably because I'd been peeing every 5 minutes all through the pregnancy anyway People at work were also saying she'd moved. Often it's the people who see you every day who notice it first.