Your first step is to talk with your supervisor. Explain to him that you like the company. Then explain that you want to grow into an SDE role, and ask him what would normally be expected and required to make that happen.
If you are in a matrix organization (I've only ever heard Microsoft use the term SDET, and I don't know how Microsoft works), talk to your project boss AND your matrix boss (think "homeroom teacher"). If your project boss and your matrix boss are one and the same, you're probably going to have to talk to both of his/her supervisors (project and matrix.)
Based on that, you decide whether it is time to start jobhunting outside the company.
Before you do that, however, understand something: an SDET can have opportunities that an SDE will never get. A college buddy of mine took a test engineer job at one of the defense airplane companies. I ran into him there, I forget if it was during my interview visit or right after I hired in. A few years later, he'd parlayed that test engineer job into a flying slot, on call 24 hours a day for when Flight Test needed an engineer to ride backseat in a 2-seat F-16. (It was hilarious. He'd had hair halfway down his back as long as I'd known him, and his beard was even longer. Then he showed up one day with SHORT hair and CLEAN-SHAVEN. When I asked "What the BLEEP?", he said "Look under the desk", and pointed at two flight helmets. I said "I'd've done the same thing.")