Half a century ago, the human race was attacked by an enemy from the sea known as the AUS. When Reiji Shiroyama was little, he was unable to protect his sister from the AUS because the gun he tried firing jammed. Since then, Reiji refuses to trust guns and only trusts his fists.
Valkyria Engine is a completed manga by Kijima Renga, first published in 2013. It blends action, romance, mecha and slice of life. You can read all 16 available chapters of Valkyria Engine online for free on MangaPulse; the newest is Chapter 14, added 2018-03-19. The series is finished, so you can read it from start to end in one go.