Well curiosity got the better of me, and the best sources I could find in ~an hour of researching suggest that they import most of the raw materials. For example, this report cites a Taiwanese source (written in Chinese), claiming:

According to statistics in the second quarter of 2022, the self-sufficiency rate of semiconductor manufacturing materials in Taiwan is 1 percent in front-end manufacturing and 15 percent in back-end manufacturing.

I don't know what exactly goes into those figures, but this overview of the supply chain for semiconductors suggests that most of the raw silicon comes from not-Taiwan which is then also refined in not-Taiwan before it makes its way to TSMC-and-co.

Three products are used as raw materials to produce wafers in step 1: high-purity silicon, silicon carbide, and germanium. If we look at the trade balance of raw materials per country, we find that Germany is the top net exporter and China the largest net importer (see Figure 7). Germany has this position thanks to high-purity silicon exports, which have the highest trading value of the three raw materials. Although silicon is the second-most abundant element (by mass) on Earth after oxygen, there are only a few deposits that can be used for high-tech applications, mainly quartz deposits (chemical: silicon dioxide). High-quality quartz sands are widespread in Germany, as reported by the Federal Institute for Geosciences and Natural Resources (BGR).

A third of global high-purity silicon exports comes from Germany (the German company Wacker Chemie is one of the largest producers worldwide), and more than 70% of German silicon exports goes to China. Although China is one of the world’s major purified industrial silicon producers (7 of the 10 largest polysilicon manufacturers in 2020 were from China), it still imports a sizable amount and is the largest net importer of high-purity silicon. The US also exports a large share of silicon (a quarter of all exports), and Hemlock, based in the US, is one of the largest polysilicon manufacturers.

Of the other raw materials, China exports the largest share, with 35% of global germanium exports and 38% of global silicon carbide exports.

Silicon and other semiconductor raw materials are melted and cast in the form of a large cylinder called an ingot and then sliced into wafers (ASML). Wafers are then used to create the integrated circuits in step 2. By comparing the trade balance of wafers with that of raw materials, we can see that the top net importers of raw materials are also the top net exporters of wafers, confirming that countries like Japan and China import raw materials for the production of wafers.

These wafers are then mostly imported by Taiwan, followed by South Korea (see Figure 9). Trade data also shows that Southeast Asia plays an active role in the semiconductor industry. While more advanced front-end chip production is centered in Taiwan and South Korea, back-end assembly is centered in Southeast Asia.

I know that that's not Taiwan-specific data but I wasn't able to find any source saying that Taiwan had a lot of high quality raw silicon to work with.

Looking at the supply chain for this is actually pretty interesting - I had no idea Germany was an important source of raw materials for example o_o