This are the files for a plug in play USB C power delivery board. The game cube uses a 12V in at 3amps at peak draw. Make sure your USB C power supply is rated for these rates. I personally use a UGreen power supply.

BOS:
USB C PD
https://www.amazon.com/gp/product/B08LDJBN8P/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1
Some type of metal connector to connect to the power pins. I used Pogo Pins but it can be wire as well.
https://www.amazon.com/gp/product/B09NHQY8R2/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1

You will have to soldier the connectors and ensure that they make contact, and that the port fits snug in the gamecube. If you use the pogo pins and they are too deep they may push the adapter out of the gamecube.The Revamped plug may assist with this but it hasn't been tested.

I am not responsible for any damages made to your console. Do your research and make it responsibly