First episode has a group of school girls in mechas fighting massive bugs/aliens, and all but one are slaughtered. Then it transitions to a young half-American and half-Japanese boy, who’s an ace pilot being sent to Japan. There are two sisters that fight in a black mecha and are crazy scary and strong, the older one at some point in the show goes on a raft and falls ill with the MC and another girl getting her and being washed ashore an island for an episode. One episode has different countries competing against each other in their mechas in a competition/tournament
Still researching, but this may be Muv-Luv Alternative: Total Eclipse.
Since 1973, an invasion of aliens upon Earth known as BETA has driven human civilization to destruction. In order to defend themselves from this enormous mass of enemy force, mankind has developed large humanoid arms called Tactical Surface Fighters and deployed them to its defense lines through out the world. However, its efforts could only slow down the impending defeat, and mankind has been forced to abandon the major areas of the Eurasian Continent. For 30 years, they have been caught in an endless war against BETA without any hopes of victory.
Now in 2001, Imperial Japan faces difficulties in the development of the next-generation of Tactical Surface Fighters (TSF) as it defends the front lines of the Far East. The UN has proposed a joint development program between Imperial Japan and the United States as a part of its TSF international mutual development unit, the Prominence Project.
Yui Takamura (a surface pilot of the Imperial Royal Guards of Japan) is given the responsibility of the project and sets off to Alaska. Meanwhile, Yuya Bridges, also a surface pilot of the US Army, heads to the same destination.
Yuya is half Japanese and half American.
Found with a search for
anime "giant robot" "half american"