Headed in the right direction, but possibly less cartoony, if that makes sense. Olympics may have been a bad example. Here are some examples of what we like:
www.crossfitcentral.com
So, doesn't necessarily have to be a person, could be a shape, a play on CFU, pretty much anything that is clean, simple and we can eventually use it on a shirt or mug without the name CrossFit Uptown on it and people will still know and understand what brand is represented.
Best of luck with your newborn!