I was just setting up the Beta testing release for the first time and couldn’t make the app visible in Play Store. Found the reason in Play Console Help:
After publishing an alpha/beta app for the first time, it may take a few hours for your test link to be available to testers. If you publish additional changes, they may take several hours to be available for testers.
After about 35 minutes the app was published.
As this might not be the issue mentioned in original question, it might help someone.