For example, I was listening to a song, and the lyric 願いや野望や空想が知らない次元【レベル】へドアをたたいて came up. Don't you usually need to use a の to make 知らない次元へのドア or else 知らない次元へ might get confused as modifying たたいて? Because of this, I'm not really sure of the meaning of the lyrics.
You are right, this sentence is normally written in this way (Let's forget the furigana レベル for now):
knock at the door leading to the unknown dimension
And because "の" is omitted, I feel this 知らない次元へ actually modifies たたく. If it were not in the lyrics, I would say such wording is at least highly unnatural. (And I might also say that hope and dream don't usually knock at the door after all.)
社長室へのドアを叩いた: OK (not necessarily the final door of the president room)
社長室のドアを叩いた: OK (the (final) door of the president room)
But in lyrics, such things can happen in order to stay in a certain rhythm. The meaning of the lyrics itself doesn't change greatly, but it may be translated as something like "Toward the unknown dimension, knocking at the door," to emphasize the "adverbial" feeling.