PeerPlay
If a tester opens your opt-in link and Google Play says the app can't be found, the most common cause is that the Play Store on their phone is signed in with a different Google account than the one on your tester list. The next most common is a closed release that isn't live for testers yet.
On PeerPlay this is one of the first problems testers report. In one paid campaign this month the very first report a tester sent was "please fix your google group, I am seeing content not available." The app was fine. The door to it wasn't. Here is how to find which door is stuck.
What the tester actually sees
The wording varies by device and by where the tester is in the flow. On the Play Store it is often "Item not found" or a message that the app isn't available. On the web opt-in page it can be a page saying the content or app is not available, or a page that never shows the Become a tester button.
A different message, that the app isn't compatible with the device, is a separate problem: the tester reached your app, but their phone doesn't meet your app's requirements. That one is about your minimum Android version or required features, not the opt-in.
Cause 1: the wrong Google account
Many people have more than one Google account on their phone. They accept your invite in the browser with one account, and the Play Store app opens with another. To Google Play that second account is a stranger, so the app doesn't exist for it.
Fix for the tester: open the Play Store, tap the profile picture and switch to the account that is on the tester list. Then open the opt-in link again in a browser signed in with that same account.
Cause 2: not really on the list
If you use an email list, the tester's exact Gmail address has to be on it, and the list has to be attached to the closed track. If you use a Google Group, the tester has to actually join the group first, and the group has to be attached to the track.
Group settings cause a lot of these reports. A group that only accepts invited members, or where join requests wait for approval nobody gives, keeps testers out before they ever see your app. Make sure anyone with the link can join, or approve requests quickly.
Cause 3: the release isn't live for testers
Testers can only install a release that has been rolled out to the closed track and has finished Google's review. While it is in review, or if it was saved but never sent for review, the opt-in link can lead nowhere.
Fix for the developer: open the closed track in Play Console and check the release status. If it is still in review, tell testers to wait and try again later rather than retrying every few minutes.
Cause 4 and 5: country and timing
Closed tracks have their own country and region availability. If the tester's Play Store country isn't selected, they can be fully opted in and still be told the app isn't available. Add their country to the track instead of asking them to change their Play Store country.
Sometimes nothing is wrong and the Play Store simply hasn't caught up. After a tester opts in, it can take a while before the app shows up for them. If everything above checks out, the tester can wait, clear the Play Store app's cache in Android settings, and try the link again.
A quick checklist
For the tester: same Google account in the browser and in the Play Store, joined the Google Group if there is one, opened the opt-in link and tapped Become a tester, then installed from the link on that page, not from Play Store search. Closed test apps don't show up in search.
For the developer: release rolled out and out of review, tester email or group attached to the closed track, group open to joining, and the tester's country selected. On PeerPlay, testers can send a Google Group Error, Broken Download Link or Not Available in My Country report, which tells you which of these to look at first.
FAQ
Why does my tester see Item not found on Google Play?
Usually because the Play Store is signed in with a different Google account than the one on your tester list, or because the closed release isn't live for testers yet.
Can testers find a closed test app in Play Store search?
No. Testers have to open your opt-in link, accept it, and install from the link on that page.
Does the closed test release need to finish review first?
Yes. Testers can only install a release that has been rolled out to the closed track and has passed Google's review.
What if the tester is in a different country?
Add their country to your closed track's country and region settings in Play Console. Don't ask them to change their Play Store country.