Yes! Here’s how to moderate messages from new members in an otherwise unmoderated group:

1. Click Management on the left side of any group page.
2. Click Messages in the "Group Settings" section.
3. Click Edit next to "Postings and Archives".
4. Select the New Members button in the "Moderation" column.
5. Click Save Changes. Now go on and moderate!

This setting means that new members to the group will require moderation for all messages they post until you change their setting to either "Use current group message posting setting" or "Messages by this member are not moderated" (the former is recommended).

This change must be made individually and explicitly for each member. There’s no set time period for membership at which point a member will automatically stop being treated as a "new" member. They’re "new" in this context until you explicitly change their setting.

An individual user's settings can be changed from either the Member Page or by clicking Edit next to "New messages posted by this member are moderated", which is in the upper-right corner of a pending message page (just above the "Edit", "Approve", "Delete", "Reject" buttons).