At the end of Cloverfield, the origin of the monster is revealed. An unidentified object can barely be seen falling from space while the characters record themselves on a Ferris wheel, months before the events of the movie.
In theory, they said it was a satellite that fell out of orbit, into the sea, awakening the monster that was asleep. I’d like to think it was the egg of the monster dropped off from a space ship near the atmosphere as kind of a “first attack”. That would make sense since in 10 Cloverfield Lane [SPOILER] the aliens are seen invading Earth with giant spaceships which I think happens very close after the events of the original Cloverfield.