Today the sauce seems totally commonplace all over the world and is so versatile in its use for cooking it seems like the perfect ingredient for spice trading. Its easy to make and doesnt go bad yet it doesnt seem like it ever really left Asia until recently (I'm assuming).
Looking into how its made it seems like everything would be readily available throughout Europe except for soybeans (I'm assuming) and even those could be brought and grown.
Wheat, soybeans, and salt and boom you have soy sauce. Were any of these things cultivated outside of Asia for this purpose? Were soy beans cultivated at all?
Finally if all of this is even remotely possible to have occurred, would the western world have had a taste for it?
Heya! This is definitely not a complete answer to your question, but it deals with an overlapping topic:
Did it ever get traded globally before the 20th century?
Yes. Soy sauce was exported from Japan and SE Asia to Europe and India in the 17th century, mostly carried by the Dutch East India Company. It was being re-exported from Europe to America by the mid-18th century if not earlier. Chinese soy sauce was being imported into Europe in the 18th century. Mid-18th century Japanese exports exceeded 1,000 litres per year. In the 18th and 19th centuries, imported soy sauce was being used as an ingredient in British-made sauces like Quin's, Harvey's, and Worcestershire.
Soybeans were being grown in Europe, North America, and India in the 18th century (maybe much earlier, but on a small scale in India). Production expanded in the 19th century.
Soy sauce was being made in Georgia (now part of the USA) in 1766, and being exported to England. For details, see Hymowitz, T. & Harlan, "Introduction of soybean to North America by Samuel Bowen in 1765", J.R. Econ Bot (1983) 37: 371. https://doi.org/10.1007/BF02904196
Despite Bowen's early Western production, modern soy sauce production in the West only started c. 1900, in Hawaii and California.
The Soyinfo Center has a lot of material about the history of soy sauce and soybean cultivation: http://www.soyinfocenter.com/index.php