Destiny's Way (The Doomed Earth Duology) by Jack Campbell

From Ace Books

 Lieutenant Selene Genji is hurled into the past to try and save a world that doesn't want her, in this action-packed adventure from the New York Times bestselling author of The Lost Fleet series.

Earth was destroyed on June 12, 2180. Lieutenant Selene Genji watched it happen. And only she can prevent it.

Thrown forty years into the past, into a time before the Universal War began, Genji can only guess what to do to change the events that led to the death of all humanity. She has no way of knowing the long-term impacts of her actions and must depend on her instincts.

But many of the people Genji is trying to save want her dead. Her creation was an experiment: a fusing of human and alien DNA. To them, she's a monster who can't be trusted, a tool of the aliens who have just made first contact.

Fortunately, she has an unshakable ally in Lieutenant Kayl Owen, who has risked everything to help her mission. Declared a traitor to humanity by Earth Guard, Owen is determined to help Genji save the planet.

Even if he dies trying.