Yes! This is totally true there is the Albany-Rensselaer station that goes straight to Penn Station which is basically where Madison Square Garden is.
You'll probably be riding the Empire Service route (there are several trains running that route including routes named Ethan Allen Express, Maple Leaf and Adirondack). You can try to navigate that here:
https://tickets.amtrak.com/itd/amtrak
If the ticket prices seem steep, then you can see if you can do one leg of it via bus and one leg by train (probably bus in, train out).