The easiest way to get close to that look would be to create an environment that has the same falloff you see in the font.
The rest is a bright metal shader with no roughness.
This looks like a pure mirror material. There is no way to bake that, or any need to do it. The look is all going to be in the lighting, color correction and the choice of HDRI background.
Blender can bake glossy materials, the reflections will just no longer move and will be static like in an old video game. You simply need to make sure the render looks like you want before doing the bake.
But if you need the reflection to actually change and behave like a real reflection, then there is no baking that will help, you will have to create a reflective material in the program where you will use this object. Or, a reflective shader could be faked with a texture mapped to reflection coordinates.