I’m getting good at dismissing the alarm and solving the Captcha and then falling straight back to sleep!
Maybe the app could keep tracking sleep sensors in the background until it detects further indication that the user is fully awake.
If it senses the user is falling back asleep within 5 minutes after dismissing the alarm it should behave like Snooze, alarm again and then another Captcha.
If it senses awake levels of activity within that time it can behave like normal.
Or an NFC tag in the shower, or even a discretely hidden one at a nearby park so you have to go for a walk or run to get to it? (I’d want to be able to use Google Play Music for my alarm playlist in the latter case).