You could try calling the temple to set an appointment; though, I'm not sure if all temples are able to make appointments by phone.
If you're going with a group, one person in the group can make a reservation for the full group.
It's not too difficult to set up a Church Account, and it's useful to have one for FamilySearch, seeing your ward directory, syncing Gospel Library annotations, etc. – so, the person could set up a new Church Account. If you are the person trying to set a temple appointment, then you already have a Church Account (it's the same account you used to sign in to post on this forum). You might need to go to
https://Account.ChurchofJesusChrist.org and make sure your membership record number is added under the "Membership" tab – this allows the website to know which ward you're in (and which temple your ward is assigned to).