Pick the times you can do, paste the link into your email, and everyone taps what works for them. When one time works for all, we email everyone the invite. Nobody needs an account.
Send this link to the group however you normally email them.
See who has answered, add more times, or pick a time yourself. We emailed you this link too. Keep it to yourself.
When all people have answered and one time works for everyone, we email everyone the time with a calendar invite. If no time works, we email you to add a few more.