First babies often (but not not always) engage before labour starts. However, it isn't unusual for them to not engage until labour starts. Other babies engage well before labour starts. With a second baby, often engagement doesn't occur until labour starts.
When a baby is engaged, it means that its head is mostly contained within the pelvis, and only a small part of the head can be felt outside of the pelvis. Women might sense this as a feeling of pressure in the pelvis, ease of breathing (less shortness of breath) and a need to pass urine more frequently.