You should be fine using your CV, references, and contracts to establish your work history. Many sole proprietors operate without an LLC. If you want a second set of eyes on your CV, I review resumes for free, shoot me a message.
Sounds like you’re in a good spot! They just want to see a solid plan, so mentioning remote work or freelancing could help. If you need a quick resume check for online jobs, I review resumes for free. Just reach out!