How did Cain go to another land and take a wife after being cast out of the Garden?

Answer:

You are making assumptions that are not in the text. Cain was Adam and Eve's firstborn son. Abel was their second son (Genesis 4:1-2). The events in Genesis 4:3 and following take place after Cain and Abel are older -- most likely adults. Genesis 4:17 implies that he was already married before the incident with Abel. There is no reason to assume that other children had not been born in that time period.

The book of Genesis is a series of eleven records. See the Introduction to Genesis. Genesis 4 falls in Adam's account. Genesis 5 falls in Noah's account. Looking back, Noah tells us, "In the day that God created man, He made him in the likeness of God. He created them male and female, and blessed them and called them Mankind in the day they were created. And Adam lived one hundred and thirty years, and begot a son in his own likeness, after his image, and named him Seth. After he begot Seth, the days of Adam were eight hundred years; and he had sons and daughters" (Genesis 5:1-4). How many other children and when they were born are not mentioned.

There were no other people before Adam and Eve. "And He has made from one blood every nation of men to dwell on all the face of the earth, and has determined their preappointed times and the boundaries of their dwellings" (Acts 17:26). We all come from Adam, including Eve who was made from Adam's rib, so we all come from one blood. That leaves no room for anyone else.

Cain married a sister. He left the area of Eden and went to another region called Nod (Genesis 4:16). He was not cast out of the Garden of Eden because he wasn't born until after Adam and Eve left the Garden (Genesis 3:24-4:1). The Garden of Eden did not occupy the whole region of Eden, it was on the east side of Eden (Genesis 2:8). We can assume he walked or rode an animal to Nod since cars hadn't been invented yet.