You traveled to 1969 in order to stop Boris the animal, he would murder your partner K, leading to the Boglodytes' imminent conquest of Earth. You went to Coney Island because you knew you'd find Boris there, but instead, you met the young version of K and he took you to the MiB headquarters.

"Now that I know what you look like when you are lying, show me how you look like when you're telling the truth?" Kay put your belongings on the desk; your weapons and your neuralizer.