No. The Sims Bustin' Out (2003, Xbox/PS2/GC) does not include pregnancy, babies, or aging.
The Sims 2 (2004) on PS2 / Xbox / GC introduced pregnancy, babies, toddlers, genetics, aging, aspirations. Full life cycle.
If you want babies on console: play The Sims 2 (backward compatible on Xbox 360/One/Series via disc) or The Sims 4 (Xbox One/Series, free base game).