To become, to come into existence, to happen, to be made. Ginomai is one of the most versatile verbs in Greek — it covers creation ('all things came into being through him'), events ('it happened that...'), and transformation ('the Word became flesh'). Over 670 NT occurrences.
The incarnation is expressed through ginomai: 'The Word became flesh' (John 1:14) — not 'appeared as' but genuinely became. God entered creation through the very verb of creation. In Genesis (LXX), God's creative commands use ginomai: 'Let there be light' → 'and light came into being.' The same word that narrates creation narrates the Creator becoming creature.