What was the Night's Watch protecting before the White Walkers?

Question

So we know from this excellent answer that the Night's King was the 13th Lord Commander of the Night's Watch, and that he fell in love with an Other/White Walker female, and somehow (yet to be told) transformed into an Other as well and became their King.

What I'm not understanding is this: why was there even a "Night's Watch" in the first place, before the Night's King and before the threat of Others/White Walkers was even known?

What were the earliest Night's Watchmen protecting the realms from before the Night's King?

Answer 1

There was no Night's Watch before the White Walkers.

The chronology of the days when the White Walkers first appeared is a bit murky, but we know that the Nights Watch was formed in response to them; Bran also built the Wall specifically to keep them out.

The First Men and the Children of the Forest initially joined forces to fight off The Others, including forming the Night's Watch to keep them at bay. Once the Others had been driven back far enough North, Bran the Builder built the Wall, with the Children's help, and set the Watch to guard it.

It was only later, after the Wall was built, that the Night's King came along. (Also, to be technical, we don't know that he fell in love with an Other, we're making that assumption based on the strong similarities in her description. There's another in-universe theory that she was the daughter of one of the Barrowmen). Eventually, he declared himself king, and was defeated by the Kings south of the Wall. As far as I know, he was never considered a "leader" of The Others (he was working with them in secret, similar to how Crastor was). That information only came out after his death.

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I should mention that the leader of the White Walkers is referred to as "the Night King" in the show, that's not the same character as "the Night's King". Both appear to exist in the TV continuity, as Ygritte recites the following story of the Free Folk on one of the DVD extras from the Second Season DVD:

About how one of your king crows found something cold in the woods... with bright blue eyes. How he brought her home, through your wall, and declared himself "Night's King". [...] With the help of the Starks, we killed the demon and cleansed your precious watch.

On the show, the "Night King" is the name given to the first White Walker, who now leads them. In the novels, the Others have only appeared rarely, and there's no mention yet of any command structure, leader, etc.

Answer 2

Note that you've tagged your question with the show tag but the "excellent answer" you link to is actually about the books. In the show we don't know who the man was who became the Night King, other than being one of the First Men, but we do know that the Children of the Forest created him:

And from that scene:

BRAN: It was you. You made the White Walkers.
LEAF: We were at war. We were being slaughtered. Our sacred trees cut down. We needed to defend ourselves.
BRAN: From whom?
LEAF: From you. From men.
_{Game of Thrones, Season 6 Episode 5, "The Door"}

From the scene, as it's the same actor, we know that the CotF created the Night King and from the dialogue between Leaf and Bran afterwards we know that they also created the White Walkers. We also know that the Night King has the power to create new White Walkers:

It's not actually clear from the show when the Wall was actually created but the wikia page states it is approximately 8000 years old, probably borrowing the information from the books. However, the show does state that the Nights Watch is also 8000 years old:

Jon Snow: We've guarded the Kingdoms for 8000 years.
Jaime Lannister: Is it "we" already? Have you taken your vows then?
Jon Snow: Soon enough.
Jaime Lannister: Give my regards to the Night's Watch. I'm sure it will be thrilling to serve in such an elite force. And if not, It's only for life.
_{Game of Thrones, Season 1 Episode 2, "The Kingsroad"}

From this we know that the Wall and the Nights Watch were created at around the same time. We know that the Wall was created to keep out the White Walkers and protect the realm from them. Therefore, it makes sense to say that the Nights Watch was doing nothing before the White Walkers because it was created after them.