The word הָיְתָ֣ה appears in the model Masoretic codices without a gaʿya on the initial ה in several places (e.g. Isaiah 1:21 in L [facsimile] & A). Likewise, זָכְרָ֥ה lacks a gaʿya (e.g. Nehamiah 13:29 in L [facsimile]). Thus, what explains that the initial qamaṣ is gadol?
I have seen some sources (e.g. Baḥur) that state that if a shewa is followed by בגדכפ״ת with no dagesh, it is naʿ. This would mean that the qameṣ is, as expected, gadol. This rule, however, appears not to be followed by most people, since it would mean that מַלְכֵֿי also has a shewa naʿ.
(I note that this discussion would be of little consequence to a Masorete, who would have no issue with accepting that the inital qameṣ is qatan. In Tiberian tradition, long vowels preceding a shewa or בגדכפ״ת without a dagesh following a shewa did not make it naʿ. Moreover, qameṣ qatan and qameṣ gadol were identical qualitatively. The qameṣ gadol just had a longer sound.)