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?

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.

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