Frankly to say Sr. Engineer has the relatively relaxed lifestyle (you do not need worry about other people’s mistake) and easier to find next job once get a layoff.
You need talk with your manager and your manager’s manager to let them know what you want. They will help you reach that goal if the chance coming.
To become the friend of those people who hold the management position which you want to become, chat with them, learn what is their life and how to handle the problems they have. This will make you ready to be a manager….
Thanks!