？
Do you remember the day we first met?
Literal
We [subject-が] for-the-first-time met day [of-の] matter [object-を] remembering?
僕たちが初めて会った ('the day we first met') is a relative clause modifying 日. Subject of the relative clause is marked with が rather than は because it's inside a modifier. 日のこと ('the matter of the day' / 'things about that day') is the object of 覚える. Casual question with no か.