MrMario2011 recently posted a guide to softmod your original Xbox without the need for a game exploit; For years, softmodding required a working DVD drive and the ability to load a game that was known to have an exploitable bug that allowed you to run code on the Xbox in an “unlocked” state. This option accomplishes what you need with either a USB drive, or Memory Unit. Links to everything you need are in the video’s description and the video has all the details you’ll need.
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And here’s a written guide on the wiki you might want to reference as well: https://consolemods.org/wiki/Xbox:ENDGAME
I’m really happy to see a solution available that can be run without a mod chip, or working DVD drive. As time goes on, it might be much harder to find either of those things and having a method that can be done with basic stuff will really increase these consoles lifespan. Maybe there have been other options available in the past I wasn’t aware of, but this one seems pretty straightforward and I definitely wanted to highlight it.
Also, please check out MrMario’s other videos! They’ve been a huge help over the years and are always my go-to for stuff like PS3!