박다 is driving something in, the way you drive a nail. 때려 박다 'smash it in' is used figuratively for ramming things somewhere with force: 귀에 때려 박는 랩 'rap that drills straight into your ears', 맛난 거 다 때려 박은 'with all the good stuff crammed in', 제가 연출한 영화에 때려 박죠 'I pour it all into the films I direct'. Half the lines here are a different word: 빼박, slang clipped from 빼도 박도 못하다 'can neither pull it out nor drive it in' — stuck, hence 'no doubt about it': 빼박 증거 'undeniable proof'.