You won't make one at home, but cloud chambers[^1] reveal individual alpha particle tracks.
There's one in the Musée des Arts et Métiers in Paris — blew my mind!
[^1]: https://en.wikipedia.org/wiki/Cloud_chamber
Edit: turns out people make these at home all the time. Sick!
This can be done at home with a little effort. Less effort if you can get dry ice easily.
https://hackaday.com/2019/01/13/see-the-radioactive-world-wi...
Well, google for "DIY cloud chamber" did result in quite some entries. Apart from youtube channels, with the first entry a guide from CERN:
https://home.cern/news/news/experiments/how-make-your-own-cl...
You can easily make them at home (source, I did last weekend!).
- Dry ice (mine came from something shipped cold)
- Dark piece of metal (I used a 3D printer hot bed) on top of dry ice to get cold
- IPA vapour (I poured some on a shop towel)
- Some transparent container to house it all - I found a glass display cube on the side of the road, fish tanks or Tupperware also work.
- Torch or something to provide side lighting
Very cool to see evidence of the particles zooming around us, can highly recommend.