I always just assumed that Clare's godmother was a wonderfully adventurous woman who--in her youth--wound up in Australia due to a random series of events. During her time there she befriended Clare's mother and they kept in touch when she returned to the states. She was only half surprised when an adorable little girl was delivered to her house one day like international post.

But...... wouldn't it Clare's transformation after she met Jack be conspicuous in an orphanage setting? I definitely don't think it would have been kept quiet.