That's an interesting and complicated question. I think it's important to note that there are many types of notations in existence throughout history, and this includes even Western notations (see link below). Some of the earliest Western music notations in Japan were drum and drum and fife scores in the mid 1800s, mainly modeled on Dutch and British military band notation systems, for example. Some examples of some of these notations can be seen here: https://robinengelman.com/2009/09/20/western-military-drums-in-japan/ https://www.academia.edu/3333316/Redefining_Western_Military_Drumming_Tradition_A_Look_at_Re_Representation_Techniques_of_Western_Style_Military_Music_in_the_Late_Edo_Period_Japan

While the Dutch actively had Indonesian slave playing Western music on the Dejima trading post probably as early as the 17th century, it's possible there might have been some kind of exchange, but unlikely given that for the most part, slave orchestras were trained by ear.

Transliteration/transcription of Asian musics into Western notation has never been a straightforward process and the history of how that happened was vastly different depending on country or region.

Here's a Timeline of Music Notation to give a sense of the breadth of global music notation systems that have existed, or currently in use, over a 4000 year timespan. https://silpayamanant.wordpress.com/timeline-of-music-notation/