Building trust with your supervisor is an art. All of us, well, most of us, want to build enough trust so we get more autonomy and responsibility in our job.
If you want to build trust with your boss, you begin with results.
Bring a project forward, get approval from your supervisor, and then get good results.
When you have a track record of producing results, you will move from getting approval to being able to do the project on your own and keep your boss informed.
Sometimes you have to test it. Pick a small project and do it. Then inform your boss of the results.
Don't wait for your boss to tell you what to do. And don't maintain exactly what is expected of you. You want to perform better than simply meeting expectation.
If you ever need clarity on where the line is, ask. Have the conversation with your supervisor so you know what issues you should bring forward and what you should handle on your own.