Anime Like Gate Keepers
A teenager stumbles into a secret war happening in plain sight and discovers he's one of maybe a dozen people on Earth who can punch holes in reality to weaponize their own power. The '69 setting is window dressing; this is really about the specific loneliness of being chosen when nobody can ever know you were. Gate Keepers treats its high school milieu and mecha action with equal weight, so you get genuine character moments between the portal-opening superpowers, which is rarer than it sounds.
SYNOPSIS
Tokyo, 1969. While ordinary citizens go about their lives, an alien invasion unfolds in the shadows. Only the covert organization A.E.G.I.S. knows the truth: creatures called Invaders are systematically infiltrating the city. High schooler Ukiya Shun stumbles into this hidden war when he witnesses a mysterious girl under attack. In desperation, he discovers he can open supernatural gates of raw power, just like she can. A.E.G.I.S. immediately recruits him, and Shun finds himself tasked with finding others who share this rare ability. Together, they're humanity's best shot at stopping the invasion before it consumes everything. The catch: Shun's late father was apparently someone important to this fight, and Shun desperately wants no part of his legacy. As he balances school life with secret military operations and clashes with his teammates, he has to figure out who he actually is separate from the shadow his father cast. It's spy action wrapped in 1960s aesthetics with just enough humor to keep things light, even when the stakes get deadly.
