Anime about girls piloting mecha to fight aliens?
The anime was basically about a group of girls who are used as pilots for these huge fighter machines to combat invading aliens. Pretty sure the machines are like sentient ancient technology from a different alien race that were also fighting the aliens invading earth. Only certain people can fight bc the machines choose their own pilots. The main girl has purple hair and she's looking for her sister who was a previous pilot that went missing during a mission a few years ago. There's other girls fighting with her and they all train together for a few episodes. There's also a girl with white hair who can communicate with the machines? I don't remember what happened but the mc finds her sister in an alien spacecraft and rescues her but her sister is stuck in a coma (and has white hair now).
Is this Ancient Girls Frame (2021), AKA Dou Shen Ji...?
At the end of the 21st century, the discovery of a new energy source called "DG energy" (short for "divine grace energy") has revolutionized Earth's economy and allowed humanity to colonize space. However, when the initial expedition reaches Pluto, they are attacked by a mysterious, giant life-form known as "Nergal."
The Earth Alliance Army fights back by creating an "AG Unit" using ancient robot weapons known as the "G's Frame" which were excavated from archaeological sites all around the world. Girls with special qualities known as "Ancient Girls" can pilot these robots against the Nergal. However, the first AG Unit suffers heavy casualties in the Jupiter Trojan campaign, and the pilot of Unit 04, Minamiya Reiu, goes missing-in-action...
Years later, Minamiya Reika, the younger sister of Reiu, enlists with the AG Unit to search for her sister and to protect the Earth from the Nergal. A story of friendship, ancient robot weapons, and battles to the death with the Nergal ensues.
As noted in the summary above, the plot involves girls being recruited to pilot ancient mechs discovered in archaeological digs, in order to defend the Earth from an alien lifeform known as Nergal.
The purple-haired main girl, Reika Minamiya (AKA Xinglan Li), is initially just a school girl, but she's chosen by one of the mechs (it finds her and beams her up into its body) and she subsequently enlists with the Earth Alliance Army hoping to find her older sister, Reiu (AKA Xingyao Li), who went missing-in-action years earlier. When she eventually finds her towards the tail end of the series, Reiu's hair has turned from purple to white. There's also another white-haired girl (called Air) in the main cast.
This was a Japanese-Chinese co-production, so the title and character names differ depending on which version you're watching.