Diving deeper into the thought while meditating is perfectly fine. It's impossible to have no thoughts and mastery comes from being away of these other thoughts coming into your mind and bring your attention back to the idea.
Good luck on your journey.
1. Make time.
2. Start with short periods of time like 2-5minutes per meditation session.
3. Focus on your breath.
4. If you notice your mind wandering…go back to focusing on your breath.
You’ll get better and you’ll thank yourself later!
You may also find guided meditation easier to work with in the beginning. Focus on the speaker, but also don't worry about your thoughts straying. If they do, just recognize it, accept it, and return your focus to the speaker.