Fix 401 errors for first-time users of PowerBI Service when using Embedded scenarios (user owns data scenario)

When a report is embedded in a web app using PowerBI Embedded (running on P capacity, embedding scenario is User Owns Data), first time users, even though they already have a Free license assigned, get a 401 error:
"Error Code: 401 Message: Http failure response for https://api.powerbi.com/v1.0/myorg/groups/***"

The workaround is to ask the user to login in the service at least once, which is very inconvenient to do for lots of users.

I suppose there can be a fix that eliminates the need for first-time users to login or a workaround to programmatically do this for every user with a free license (REST API, PowerShell, etc.).