That's a really good question and I wish I knew the answer. The earliest that I can find it showing up on-stream is in episode 1x18, Trial of the Take: Part I (streamed on 30 July 2015), where the neon light behind Laura is definitely the logo. In a tweet (https://twitter.com/matthewmercer/status/621119948580982784) on 14 July 2015, Matt also refers to the first Critical Role logo t-shirt being available now, and the Wayback Machine indicates it was on the G&S webstore as early as the 11th.

All of which doesn't answer your question, I know, and you probably already knew it. My personal best guess is it was someone in the G&S back office, but it could very well have been based on a sketch by someone else. If you ever find out, let me know!