Context: Hey look! The Golden Gate Bridge! Isn’t that great?! It’s not made out of solid gold like we thought, which is kind of a disappointment, but still! Does this sentences make sense ?
It's not like we think.
It's not like we thought.
It's not like we thought.
Is correct.
Thought, used here, is the past tense of think.
Since we have now seen the bridge ourselves we no longer think that it is made of gold. But, in the past, we thought it was.
It's not like we think
is also a correct sentence, but has a different meaning - the group would be berating themselves for making a silly decision, possibly involving sarcasm.