My suggestion is to book the later Amtrak departure. If things work out such that you can make the earlier departure, make your way down to track level and tell an Amtrak conductor on the platform that you are booked on the subsequent train, but your flight got in early enough for you to make the earlier train. Ask if you can be accommodated on the earlier train. If the conductor says OK, you're golden; if the conductor says no, then you can go back upstairs, pass through the fare gates again, and get a doughnut, while you wait for your ticketed train.

What is your Amtrak destination?