Buddha?..
'In the Wiradjuri language (Albury to Dubbo area), sandalwood is known as budha and used for its therapeutic, spiritual, and practical benefits'.
'Kamilaroi language (Dubbo to Goondiwindi) has the term badha for Bastard Sandalwood, distinct from the commercially prized Australian Sandalwood, because it has a similar oily, aromatic wood to the true sandalwood, but is a different genus species'. The budha, badha names are explained by two histories from Aboriginal countries about boats that arrived.
This is the boat at Illawarra. https://library.kiama.nsw.gov.au/History/First-Nations-Kiama
This one was at Yamba and Lennox Head.https://planetcorroboree.com.au/blogs/culture-country/the-three-brothers?srsltid=AfmBOoroDdoE9ct1CQ3-u4-eislVXzZi-jsSkuAdgvKh-xr4ZogoEQaD
The Dharawal boat came from Ngarawan from the east which may mean it was observed landing from the east. Ngarawan is a locality today north of Java. The Bundjalung boat came from Ngareenbeil (J Isaacs. Australian Dreaming p 13,14) and means 'your beloved countryman' in Old Bali language (Darma Putra. School of Languages, U Qld). Old Bali is a form of Old Java, used between 800-1500 CE. Bundjalung has ngarihngbil 'foreigner, person from other side, stranger, someone from another tribe or country.'
The Javanese Majapahit empire of 1292-1527 was a Hindu-Buddhist state and sent Brahmin priests to the islands. Evidently some Buddhist teachings were brought. Dharawal budaya 'good, righteous'. Bundjalung budjagah 'fig tree'. budjaram 'legend, sacred thing'. Wiradjuri budhurbudhur 'a smell.' budhana 'to smell'. budhabara 'sandalwood smoke'. bara 'scent'.
...but there's more...