Shuu and Masaki have a lot of history - it hasn't been totally flushed out in the OG games yet, but this is how it was in the other games that they've appeared in (other games of the SRT series, namely the "Classic" timeline of SRT 2-3-EX-4/F/FF) and the Masoukishin games (which means, "Lord of the Elements", and the Cybuster is the "Lord of Wind" and Masaki it's chosen pilot). Their origins take place in a sub-dimensional world within Earth, La Gias.
Just a reminder, timeline-wise, these events have already taken place in the OGverse (occuring before the events of OG1).
Shuu's mom is "kidnapped" by a member of the Royal Family of Lan Gran (one of the 3 kingdoms of La Gias) and is made his consort/concubine, and Shuu is born some time afterwards - thus, Shuu is half Earthian, half La Gian, and a legitimate heir of the throne of Lan Gran. He grows up to value his independence much more than anything (most likely stemming from his mother's freedom being stripped from her since she was kidnapped), and thus has no interest of the throne. Shuu travels back-and-forth from the surface world, and becomes the genius he is as he absorbs knowledge from the surface AND La Gias, using this knowledge to build the Granzon.
Masaki (a orphan) is mysteriously transported to the world of La Gias (people are summoned frequently, actually, as people from the surface tend to have higher prana levels) and ends up being taken in by the people of Lan Gran. He gets trained by the King's Retainer, master swordsman Zeoroot and becomes his (Zeoroot) adopted son. He ends up as the chosen to pilot the Cybuster (as in, the Cybuster chose him to be it's pilot, and it's always been known as "picky"). He meets the other 3 Masoukishin pilots (Fire, Water/Ice, and Earth), who are also pilots from the surface world. During a trip back to the surface world, Masaki meets Shuu and the Granzon, with Shuu already knowing about Masaki and the Cybuster (Shuu had originally been in line to attempt a partnership with Cybuster, but Shuu didn't care about it and built the Granzon instead). Shuu suggests that Masaki return to La Gias, as the Earth Federation would most likely be coming after him as Masaki is a "unknown" (this is before OG1, where the EF learns about the Cybuster).
Masaki already has a bad vibe about Shuu from this meeting, and it becomes true when the Granzon attacks Lan Gran. Shuu, for one reason or another (depending on the Classic Timeline, or the Masoukishin games) has aligned himself with Volkruss (god/demon of destruction/chaos), and declares war on Lan Gran, attacking the capital. Masaki fights him, gets his butt whipped, and is forced to watch as Zeoroot battles Shuu. Zeoroot is killed, and Masaki gets pissed off, becoming semi-possessed by Cyfis, the Lord of Wind that "blessed" the Cybuster. With this boost in power, the Cybuster is able to turn the tables on Granzon (who's Warp field barrier was also damaged by Zeoroot's last-ditch gamble), and Shuu is forced to retreat. The semi-possession almost kills Masaki (Full Possession would kill him), and he is saved by a last-minute prana-transfer from Wendy, a princess of Lan Gran (and possible love-interest). Shuu goes back to the surface world for repairs (with the help of Bian and the Divine Crusaders).