When is the soonest time I can induce labor?

39 weeks. Labor can be induced at anytime. Sometimes we even induce prematurely if the mom or baby are in danger. There are risks of prematurity though. These risks seem to be lessened after 38 completed weeks. So we try to wait until after 39 weeks to induce someone electively.
Ask your OB. It depends on your individual circumstance and if the babies lungs are developed enough.