While the Greek prefix ἀν- can certainly possesses the meaning of repetition (i.e., “again”), it can also mean “up.” Hence, the lemma ἀνοικοδομέω can be used in the sense of “to rebuild” but also “to build up” (i.e., a home is built from the ground up[wards]).

Accordingly, LSJ defines the verb ἀνοικοδομέω as,

>A. **build up**, “τὰ χείλεα τοῦ ποταμοῦ . . ἀνοικοδόμηδε πλίνθοισι” Hdt.1.186. 
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>2. wall up, “λαύρας καιναῖς πλίνθοισιν ἀ.” Ar.Pax100; “θύραν” Lycurg.128; πύλας dub.l. in D.S.11.21 (in this sense ἀποικ- is a freq. v.l.). 
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>II. build again, rebuild, “πόλιν καὶ τείχη” Th.1.89, cf. Jusj. ap. Lycurg.81, X.HG4.4.19, etc.; “ἀ. χώραν” occupy again with buildings, D.S.15.66:—Pass., metaph., to be exalted, LXXMa.3.15.