。
She looked like she was about to burst into tears.
Literal
She [topic-は] at-any-moment cry-burst-out [appearance-そう] was.
泣き出す is a compound verb: the masu-stem 泣き ('cry') plus the auxiliary 出す ('start to, burst out into'). The auxiliary 出す productively turns verbs into 'sudden start' compounds — 走り出す ('break into a run'), 笑い出す ('burst out laughing'), 降り出す ('start to rain'). Combined with 今にも~そう, the phrasing captures the precise moment of being on the brink. The whole sentence — 'on the verge of bursting into tears' — packs imminence (今にも), sudden onset (~出す), and visual inference (~そう) into one tight construction.