Heh, that's a fun point. Maybe even a deep point. They don't have to leave a long trail of artifacts of incremental groping toward the concept of written language, starting with seal icons and tally marks and then account ledgers and then complaint letters. Instead, somebody could just have the idea, all of a sudden, if conditions are right to suggest it. Or several people could. But this raises the question of how big an idea it's possible for one person to have all at once, without handing it between multiple people in evolutionary stages. I guess there's no real limit on that, it's just that excellent ideas require excellent zeitgeist conditions (like the availability of paper that you mention).
So... The "big idea" would be "a writing system that fully represents a language."
Everything else can develop gradually. But... gradually doesn't necessarily mean generations. It can be one person expirementing, working on the project and until completion.
Think of it as a "master work" or a PhD. Big, but not beyond the right person's ability to complete over a decade.
Think Newton, Galileo or Tolkien. They didn't just "have an idea" that fully worked. But... they worked on their ideas for years, got a lot done themselves, and had fruitful projects.
People are people. What is possible in one century is possible in another, unless prerequisites are not present.
In the case of language... the centuries of development mostly contribute the ambition itself.
The inventor may not be doing some great project. They might be just inventing something small to help keep track of sales... or they're just inventing a gambling game that uses symbols.