Speaking of Ozymandias and co. trying to prevent the world from falling into a nuclear holocaust, it becomes abundantly clear in the first few pages of Doomsday Clock #2 that time is of the essence.
Ozymandias explains that he had figured out a way to track Doctor Manhattan via the electron trail he left after leaving their Earth, he, Rorschach, the Marionette, and the Mime, prepare to embark on their inter-dimensional journey in the modified Owlship. However, just a they are about to embark on their journey to New Earth, the nuclear bombs begin to fall on the city of New York.
In other words, Ozymandias' greatest fear, which lead him to carry out his deeds in the original Watchmen novel, have finally come true. As he and his cohorts set out, his world is just beginning a nuclear war. This makes it abundantly clear how important it is that they succeed in their mission to retrieve Doctor Manhattan, lest their world be irreversibly doomed.
The fact that the entirety of the original, twelve-volume Watchmen book was about preventing nuclear war, whereas in Doomsday Clock, one has begun on the second issue, shows just how dire the situation in the Watchmen universe is. It was implied that the bombs were fast approaching in the first issue, but seeing this actually unfold in the second was still incredibly harrowing.