It is definitely not by sheer luck that Nausicaa helps Odysseus. Her involvement is carefully and deliberately orchestrated by Athena. Athena was very fond of Odysseus and protected him during the Trojan War. However, after the war, Odysseus lost his way during his voyage back home and was taken captive by Calypso. Athena demanded his release through Zeus, and Odysseus was allowed to leave by Calypso. His destination was Scheria the land of the Phaeacians. On arrival, Odysseus was completely exhausted and needed some help finding his way to the Phaeacian town. Nausicaa was the daughter of the Phaeacian king, and Athena planned her meeting with Odysseus by appearing to her in a dream. Athena convinced Nausicaa to go to the waterside where he would meet with Odysseus and introduce him to the king.
She went straight to the beautifully decorated bedroom in which there slept a girl who was as lovely as a goddess, Nausicaa, daughter to King Alcinous. Two maid servants were sleeping near her, both very pretty, one on either side of the doorway, which was closed with well made folding doors. Athena took the form of the famous sea captain Dymas' daughter, who was a bosom friend of Nausicaa and just her own age; then, coming up to the girl's bedside like a breath of wind, she hovered over her head
it is certainly not pure luck that Nausicca helps Odysseus. It is mostly the work of Athene combined with Nausicca's own character and Odysseus' wisdom. First the reason that Nausicca is even present to find Odysseus by the river is because Athene suggested that she go and do the laundry as a dutiful daughter. When Odysseus emerges from the bushes he at least has the sense to cover his private parts with leaves, then when he has the chance to speak with Nausicca he refrains from throwing himself at her feet which would have probably scared her away, and speaks from a distance. Nausicca herself shows great bravery by remaining to speak with Odysseus after all of her servants run away. Finally, when Odysseus is given a bath and clothing, Athene enhances his appearance so he appears to be a God, so that Nausicca would want to continue to help him.