Alex discovered Angel was his daughter when she directly revealed her true identity to him after they had spent a night together. This revelation came after an earlier, significant encounter where he had failed to recognize her as his child.
The Unrecognized Connection
Prior to the definitive revelation, Alex was actually brought to his daughter. However, during this earlier meeting, he did not realize or acknowledge that the person before him was indeed his own child. This highlights a missed opportunity for recognition and sets the stage for the dramatic disclosure that would follow.
The Moment of Truth
The pivotal moment when Alex finally learned the truth about Angel's lineage occurred after they had spent a night together. It was during this intimate period that Angel chose to tell him who she truly was, bringing the long-unrecognized familial tie to light. Her direct confession served as the definitive way Alex came to understand that Angel was his daughter.