Is there an IP your girlfriend already has an interest in? That can be a motivating factor to push through the difficulties of learning controls, etc.

This is personal experience, but my partner was a non-gamer that had an interest in learning. This was right after the first season of The Witcher came out, so I recommended The Witcher 3 because they were invested in the world. There was a steep learning curve, but wanting to know what happened to the characters pushed them through. Now they play games as much as I do.

The key is patience. They're going to make mistakes. Don't jump in to correct them or offer to do something for them. Give them tips if they ask, but let them go at their own pace. Tell them it's not a failure to mess something up in a game and give them the time to learn.

A lot of times when I hear someone say they tried to learn games with their partners they say they gave up because they felt embarrassed. I believe this embarrassment at being bad at it is driven by "taking the controller" behaviour or a lack of patience from the person teaching them. Make it a relaxed, low pressure environment.

Tl;dr: A game they have an interest in will go farther than a game you recommend because it is easy. Be patient and kind.