How do timestamps work with the blockchain and difficulty adjustment?

Hello! :)

As I understand, every block has a timestamp that indicates at what time the block was successfully mined. And this is used every 2016 blocks to adjust the difficulty, in order to achieve an average of 10 minutes per block every two weeks.

But, how does the network really know if the timestamp is accurate?

How does it know if the miner is mistaken or lying?

You can check for invalid transactions with math, but how does it verify the timestamp without trusting in a third party?