There's no menu exploit for Gamecube. Super Smash Bros is one of several hackable games.
On every boot, you must use a commercially produced disc with valid region code to initialize homebrew.
Once a loader program like Swiss is open, then burned games may work. If the system's laser cooperates.
A modchip is more flexible. Drive chips allow loading homebrew directly from a burnt disc.
Other kind of chip have options like SDgecko or an internal SD card slot. Game compatibility varies somewhat depending on the method.