How did you buy the tickets? Unless we are talking RailSale, Ebay, or another heavily discounted fare, you should always be able to simply reserve a sleeper (first-class) at the time you make the reservation.
However, to answer your question, you can upgrade accomodations once onboard ANY Amtrak train, based on availability, of course. Many times no rooms will be available, or will only be available for part of the trip/night (someone else has a reservation to an intermediate point; this part doesn't apply to Auto-Train), so always be prepared to spend the night in coach. Check upon (an early) arrival to have the best chance of snaring a room. The prices will be very good, much less than buying the accomodations at reservation, but you take your chances.