As Mary mentioned, you do wait at the exit for this attraction. Usually, the wiat will be at least several ride cycles and, if it is busy, they may give you a handwritten Fastpass and ask you to come back.
You will be brought into the boarding area at about the same time as they open the gates to let oth guests into the ride ara. Since teacups are to assigned in any way, as soon as the gates open, guests start Heading toward the teacup of their choice. When we have ridden, we often find that someone faster is heading toward the same teacup as we are, and they often get there first. So, I would suggest sending a faster member of your party ahead of you to get a teacup.
There is no more accessible tacup. Each has about 6 inch step up over the edge of the saucer to a somewhat level part of the saucer, then about an 8-10 inch step over the side of the teacup. The teacup has a very narrow opening.
At the end of the ride, the teacup may not end up in exactly the same place as it started, so you may have a longer or shorter walk.