This tale was previously adapted into the 2010 animated movie Superman/Batman Apocalypse, and while a completely faithful adaptation probably wouldn’t work for the big screen given that it’d be difficult for Batman and Wonder Woman to be involved, as long as Henry Cavill’s Superman is at least around, with some creative shifting, this could serve as a cool origin story for Kara.
After she died during the Crisis on Infinite Earths event, Kara Zor-El only appeared sporadically in the DC universe until 2004, when she was reintroduced in the Superman/Batman series.
In this continuity, rather than their familial relationship just being a cover, Supergirl and Superman were actually biological cousins, and when she landed on Earth, not only did Kal-El help her acclimate to Earth, she was also mentored by (an initially distrustful) Batman and Wonder Woman.