It seems that after cards are archived, they are removed from the boards they were associated with. I'm hoping that's not the case and that various metadata about the cards are tracked. What I want to be able to check is the state of a list (or board) at a specific timestamp in time.
No to "snapshot in time", Your Trello board is always a current version of your items (lists, cards) as they are now.
Your Archived cards are still stored within the board. Once you Archive a card, it is stored in "Archived Items" under the board Menu with all of the other archived cards.
There is no way to go back and see any previous state of your boards. Always move forward.