1 The Lord had said to Abram, “Go from your country, your people and your father’s household to the land I will show you.
2 “I will make you into a great nation,
and I will bless you;
I will make your name great,
and you will be a blessing.
3I will bless those who bless you,
and whoever curses you I will curse;
and all peoples on earth
will be blessed through you.”
At the outset, there was no specific promise of land, only nation or גּוֹי (H1471 goy) which could mean people.
This was in step with God's practice of gradual revelation.
The promise of land and offspring came one chapter later in
14 The Lord said to Abram after Lot had parted from him, “Look around from where you are, to the north and south, to the east and west. 15 All the land that you see I will give to you and your offspring forever.
Naturally, Abram understood the promise that he himself would receive at least some land.
A few years later, Abram wasn't getting any younger, but still no land and no offspring. On top of that, Genesis 15:
7 He also said to him, “I am the Lord, who brought you out of Ur of the Chaldeans to give you this land to take possession of it.”
8 But Abram said, “Sovereign Lord, how can I know that I will gain possession of it?”
Why all of a sudden
It wasn't all of a sudden, it was a few years.
does Abraham need some kind of evidence for believing that God will fulfill His promise to give Abraham this land when Abraham had already walked over 500 miles because God told him this was the land he would give him in chapter 12
God didn't promise him the land in chapter 12.
and when he had enough faith to believe God's promise to give him a son through his wife in the verses leading up to Genesis 15:8?
Actually, the promise wasn't really that precise and clear. Even at this point, Abram had no idea that he would not take possession of the land and only his descendants would do so hundreds of years later.
To fortify Abram's faith, he would perform a ritual to verify an agreement of covenant:
9 So the Lord said to him, “Bring me a heifer, a goat and a ram, each three years old, along with a dove and a young pigeon.”
10Abram brought all these to him, cut them in two and arranged the halves opposite each other; the birds, however, he did not cut in half. 11Then birds of prey came down on the carcasses, but Abram drove them away.
Abram had everything, waiting on God's move next.
12 As the sun was setting, Abram fell into a deep sleep, and a thick and dreadful darkness came over him. 13Then the Lord said to him, “Know for certain that for four hundred years your descendants will be strangers in a country not their own and that they will be enslaved and mistreated there.
God revealed more detail of the contract.
14 But I will punish the nation they serve as slaves, and afterward they will come out with great possessions. 15 You, however, will go to your ancestors in peace and be buried at a good old age.
Abram learned that he himself would not possess the land.
16In the fourth generation your descendants will come back here, for the sin of the Amorites has not yet reached its full measure.”
17When the sun had set and darkness had fallen, a smoking firepot with a blazing torch appeared and passed between the pieces.
This was a supernatural sign that sealed the agreement. God had just signed the contract.
18 On that day the Lord made a covenant with Abram and said, “To your descendants I give this land, from the Wadi of Egypt to the great river, the Euphrates— 19the land of the Kenites, Kenizzites, Kadmonites, 20Hittites, Perizzites, Rephaites, 21Amorites, Canaanites, Girgashites and Jebusites.”
How does what follows immediately after verse 8 provide any more evidentiary support for Abraham beyond the Word of God he had already received, on the cause of which Abraham picked up and traveled over 500 miles and believed that Sarah could bear him a child?
The supernatural fire was the sign that ratified the covenant agreement. It's God's signature on the contract between God and Abram.