The Gate of Eden
I think a compelling case can be made that the phrase, “Sin is crouching (רֹבֵ֑ץ) at the door (לַפֶּ֖תַח)” in Genesis 4:6 refers to the gate of Eden (and the serpent crouching there). The main thrust of this argument is that the word “crouching” isn’t very common in Genesis, only appearing four times outside of this instance. Importantly, the next time it shows up is in 29:1-3 when we see Jacob journeying to “the land of the people of the east,” wherein he sees “a well in a field” that “waters” the flocks of sheep, and it’s guarded by a “large stone,” beside which the sheep are “crouching” (רֹבְצִ֣ים). That this is a clear allusion to the garden of Eden should be obvious. The garden was “planted in the east” (2:8), its rivers “watered” the earth (2:6-10), and after the Fall, its gate became guarded by a flaming sword (3:24). Thus, that the sheep were “crouching” at the entrance to this well tells us that Sin was also “crouching” at the entrance to Eden in the days of Cain.
Moreover, the word used for “door” in 4:6 is interesting because, throughout Exodus, Leviticus, and Numbers, it’s used to describe the “door” or “entrance” (לְפֶ֣תַח) to the Tabernacle (Exodus 26:36, 29:4-42, 33:8, etc.); and this is significant because the Tabernacle represented the garden, hence why the Levitical priests were told to “keep and guard” it (Numbers 3:5-7), just as Adam was to “keep and guard” the garden-sanctuary (Genesis 2:15), meaning that its “door” corresponds to the “door” or gate of Eden, a point solidified by the fact that, right before this, Jacob was shown the true “gate of Heaven” in a dream (28:17).