Whereas aussi as a sentence adverb (adverbe de phrase) indicates that what follows proceeds from what was said as it's virtually included therein, aussi bien detaches what follows and marks it as self-explanatory, says the TLFi. Larousse marks a similar construction, introducing an accessory causal element, as literary; Ac.9 says classical. LBU14 §1034 says it's more frequent than that and discusses it: saying it generally introduces an explanation, a further justifying, sometimes being closer to the meaning of en effet and some other times to d'ailleurs, au surplus, tout compte fait. Modern : "Ne croyez pas que je vous en veuille. Aussi bien je veux être joyeux aujourd'hui" (Gide); classical : "Je n'iray point, aussi-bien il est trop tard." (Ac.1694) Compare with aussi bien as a locution adverbiale ("Car aussi bien se véoient-ilz perduz"). This is further complicated by the fact that you could find in classical texts aussi alone used like so and not necessarily at the beginning of a sentence, albeit with a stronger causal link : "Entre les morts, on ne le put trouver : / Le roi de Perse aussi l'avait fait enlever" (Corneille), au LBU.
To summarize, the difficulty is about the scope of the adverbial use of aussi bien (full sentence, construction with que etc., or expressions) and its evolution. If it were to mean en effet in your example, it could possibly translate to indeed (Collins); au surplus could yield moreover (Larousse). Nice one.