sharing – How can I share calendar with a link only

I would like to share a Google Calendar using a only a link to members of my organization, so they subscribe to it.
How can I get this to work?

Constraints:
Not all users have Gmail addresses and they do not want to get one.
I do not want to make the calendar public.

Previous efforts:
I have tried sending them the private ics address from settings, but while they can view past events, they cannot view new events after their subscription.

Alternatives:
If these requirements can be satisfied using another calendar service, we can switch to one that does. Please suggest one.