I'm trying to open a Sketch format file in Illustrator but Illustrator doesn't support it... How can I convert it to a vector format that Illustrator supports?
I only have Windows so cannot install Sketch to export another format.
Illustrator doesn't open Sketch files. You'll need to open it in Sketch and export it to a vector format that Illustrator supports; namely PDF, EPS or SVG.
Which format you use depends on your artwork...
Note: Some effects you can perform in Sketch are not supported by all vector file formats, including transparent gradients in PDFs, and inner and outer borders in SVGs.
...If you don't have access to Sketch (or can't get whoever gave you the file to give it to you in a useable format; which would be the best option) you could try...
You could also try something like https://convertio.co/sk-ai/ which claims to convert Sketch files (I don't have Sketch installed to try, but it works OK with other formats).
Exporting from Sketch as SVG using the Export controls in the Inspector (right side panel) worked well for me. Illustrator opened the exported file with the named layers and groups intact, exactly as they were set up in Sketch, and the file behaved as if I had created it in Illustrator. I was using Sketch 52.5 and Illustrator 23.0.1.