Back in 1787, more than 200 years ago, the United States of America didn't exist the way it does today.

the way it does today.在此是方式状语从句，由the way引导。名词the way在非正式语体被用作从属连词。类似于the moment引导之间状语从句。

《韦氏高级词典》

the way

informal 非正式用词

1— used to say what someone's way of speaking, behaving, etc., seems to suggest

• You'd think she was rich, the way she spends money! [=she spends money like a rich person]

• The way he talks, you would think he ran the company. [=he talks as if he were the person who runs the company]

2 — used to say that something happens or is done with the same attitude, at the same pace, etc., as something else

• They replace their cars the way [=like] other people replace shoes.