You can start now without making a dramatic change. A little familiarity can help you ask better questions when AI comes up at work or in a service you use. Starting does not require buying a course, changing careers, or adopting a tool immediately.
Choose a small first step that fits your circumstances. Read an introductory explanation, watch an approved workplace demonstration, or test a non-sensitive task you already understand. The right pace is one you can sustain while continuing to meet the other responsibilities in your life.