The underwater city introduced in Godzilla: King of the Monsters is said to be the MonsterVerse's oldest civilization in history. After Godzilla was nearly killed by the Oxygen Destroyer, Monarch explored the depths of the ocean to enter the Hollow Earth tunnels. There, they found evidence of an ancient civilization.
Murals on the walls revealed that the people who lived there worshiped Godzilla and the Titans as gods. It was suggested that during this time Godzilla and humans were able to co-exist. Though it's been thousands of years since the city was destroyed and forgotten by history, Godzilla still feels a connection to this place, which is why he retreats there after being badly wounded. Whatever this place was, it was the home of Godzilla, and possibly classic Toho monster Anguirus as well. Unfortunately, it was destroyed by the nuclear bomb set off by Dr. Serizawa (Ken Watanabe), which was used to revive Godzilla.
The redacted text in the credits of Godzilla: King of the Monsters reveals some interesting information about the long and complicated history behind the relationship between humanity and Titans. An expedition made into the Hollow Earth tunnels by the U.S.S Scorpion submarine led to more details being uncovered about the ancient culture. Footage from the submarine has confirmed that the underwater ruins "predate all known civilizations".
This elaborates on some of the comments made by Monarch scientists during the movie. When Mark (Kyle Chandler) remarks that the paintings on the walls look similar to those associated with the ancient Egyptians and the Romans, Dr. Chen (Zhang Ziyi) says that this culture is much older than either of them. This is a bold statement to be sure, considering that both the Romans and the Egyptians are accepted by historians as two of the oldest known civilizations. Another culture that comes to mind when thinking of the oldest known civilizations is Mesopotamia, which dates back 10,000 years, but apparently the underwater city is even older than that. In fact, it may even be the mythical city of Atlantis.
What happened to this place, and how was it forgotten for so long? As the redacted text explains, a war erupted between the humans and the Titans after the humans tried to enslave them. The war triggered a "cataclysm", which is why so many different civilizations around the world fell. This, followed by other geological catastrophes could be what caused it to become submerged deep in the ocean as seen in Godzilla: King of the Monsters.