It sounds like you've already identified your weaknesses, and they are EXTREMELY COMMON - especially for really great engineers.
You used the word entrust, and this is key. It demonstrates that you have a great sense of ownership over the work, and feel personally responsible for the team's output. This is great, but now that you are the team leader and not the team itself, you need to get three additional ideas burned into your brain.
1: The members of your team are working with you toward a common goal, but they are not performing brain surgery on your first-born child. A little imperfection and inefficiency is OK. In fact, it's good business.
2: It is your job to set that common goal - which must be based on a business goal - and get the team to buy into it. Getting buy-in is, ironically, more a function of how well the individuals on your team believe you hear their opinions than how well they hear yours, so this is a great opportunity to practice your listening skills. But once you are all focused on the goal, the fact that someone solved a problem differently or more slowly than you would have will bother you less, because you will know you were doing other important stuff at the time and together you got closer to the goal than you would have alone.
3: Innovation means trying things and learning from them. The more people on your team try things, the more you all get to learn, so give them the space to try and celebrate the process as a team. Yes, sometimes that means people will try things you already know won't work, but sometimes you will learn a better way, or fail in a new way that leads to a new success. None of it will be a waste of time.
Finally, remember that these apply to your own performance on the team as well. Allow yourself the time to experiment and learn as a manager. Listening, delegating, and coaching are all learnable skills that require practice more than study, so just work at it and know that you'll get better at it.