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Has anyone been able to get a letter of intent with just an idea? Is that even possible?

Second time founders get this sometimes, if their first startup was a success. Basically, they've already proven they can execute.

Yes.

would you like to share your story of how you did it?

There's no real "how you do it" other than having friends with money. I've seen LOIs with an idea range anywhere from $10k to $1M.