Answer: There is nothing in the text itself that implies that Cain tried to get back into the Garden of Eden, and it is not the reason he was at the gateway of the garden.
Once Adam and Eve were expelled from the garden, God placed at least two cherubs to guard and block the entry. Furthermore, there was the flaming sword. This sword was not a compass, but the Shechinah glory, the visible manifestation of the presence of God. This arrangement stayed the same until the Noahic flood destroyed the Garden of Eden.
Adam and Eve knew about God’s presence being at the gateway to Eden, which is why they would bring their offerings and sacrifices to the entry of the garden, and it is the reason why Cain was there too. However, he could not get in with the cherubs guarding the gateway. After God judged Cain for killing Abel, Cain left the presence of the Lord (Gen. 4:16), meaning he went away from the area where the Shechinah glory was to a distant place. He probably never returned.
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Arnold Answers is a bi-weekly Q & A with founder and director of Ariel Ministries, Dr. Arnold G. Fruchtenbaum.