First, congratulations on your approvals.
As to InfoPass, you have to use it in the morning. When all appointments are taken, then InfoPass stops, and you have already saw the display message. It has a two-week window. For a work day (appointments only in 1,2,4,5), new appointments are available after midnight (might be 1am). They are pretty much all gone after 11am. So, if you schedule now, you can only get an appointment for two weeks later. If for only one person, you might try the InfoPass frequently trying to catch one that somebody else canceled. But it might not be easy for all family members.
Also, you have to make individual appointment for each family member. I read here, many people were turned down because they did not do that.
Another inconvenience is that it won't allow you to schedule again in half an hour after one appointment.
My 485 was approved on 5/21. PP scheduled on 6/11. Rescheduled to 2-weeks after 6/11.