In order to obtain GE, you will need to obtain a passport. That entails application and photo fees. You will then need to apply for and obtain a GE card. That entails a $100 fee + physically going to a CBP interview.

For that, you will have the chance that you will have a faster and less PITA experience at the checkpoints for your trip to/from DEN. And, remember it's just a chance to qualify for the expedited screening --- not a guarantee.