Run Auto Parts, VAGParts and Automotive Superstore are my main go-to's for suppliers in Australia. Note that Automotive Superstore are quite generic (covering all bases) so mainly only look to them for things like brake disks etc. Sparesbox is another generic one.
For specific stuff (stuff that I know will be hard to source locally) I usually get the part number and search on Google or ebay. For example, I recently got some new exterior trim pieces for my nearly 10yr old Audi SQ5 and ordered them via ebay from a shop in Latvia - all brand new genuine parts in original packaging but just shipped from Latvia. Ive ordered a lot of parts over the years from USA, UK or other areas of Europe.
The issue you will have with your Cupra is that because its such a new car, a lot of websites will either not have your car listed, or if they do - they wont have much to offer. You are best to get part numbers and then Google/ebay those specific part numbers. Like you have already found out, lots of the parts used on your Cupra will also be used on various other VW/Audi models so you can cross reference part numbers.
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