Yes, a full-size mattress can fit in a Sienna. There are three ways to do this:
1. Remove the seats. This will give you plenty of room to slide the mattress in.
2. Fold down the back seats. This won't give you as much room as removing the seats, but it's still enough to fit a mattress.
3. Take out the middle row of seats. This will give you the most room to maneuver, but it also means that you won't be able to have any passengers in the back while you're transporting your mattress.
Whichever method you choose, make sure that you secure the mattress so that it doesn't move around while you're driving!