Needless to say they were unsuccessful, but after dropping a hydrogen bomb on Godzilla, the creature disappeared for 60 years, and subsequently Monarch was formed to study him and other monsters.
Although initially believed to be dead, Godzilla awoke the next morning and returned underwater.
Godzilla returned in the 21st century when the first MUTO (Massive Unidentified Terrestrial Organism) surfaced, and with some human assistance, he defeated his adversaries before they could reproduce.
In his first MonsterVerse appearance, we learned that Godzilla was first awakened accidentally by an American nuclear submarine, leading the United States military try to kill him using nuclear bombs.