You can't see it via the regular achievements list on the console, nor the Xbox app or website.
If you have it unlocked, you can pin it to the top of your activity feed by doing this: -
1. Find a gamer who already has it pinned to their feed. They don't have to be a friend - they just need to have it pinned to their feed. I have it pinned to mine.
2. Go to their feed and click on the pinned achievement, then click on "Xbox One - Go to official club" on the right.
3. In the club, navigate to the Progress tab and there you will see your own Day One achievement unlock.
4. Click on the achievement, click on "Share", then you can share it to your own activity feed.
5. Go to your own feed, click on the achievement, then pin it.
I do agree that it would have been better if they added it as a profile badge when they removed it from the regular achievements list, especially as only 0.66% of Xbox One owners have it, but I think that ship has sailed already and they're unlikely to do anything with it now.