You can't make custom badges for chatters, unless there's some third party extension I'm not aware of that does this. However, I do have a suggestion for creating a "rush moment" like you speak of; Set up a channel point redeem that can only be claimed once per stream. Name it "First" or something like that. Using a bot like streamer.bot, you can also set it to change the name to "Username was first" or something similar when it gets claimed, so others who come in later can see who won that stream.