I have done 50mm thick fibreglass with infusion where we used the flow medium on each side of the stack. All went well, it was water jet cut to a profile after.
If you need such a structural part then machining it from solid carbon may not really be the best way. I would assume your block is a uniform laminate of x? layers of possibly the same material? When you machine this you would be cutting through the fibres and layers at the surface of your new part whereas a moulded part can have some of the layers essentially wrapping it up in an unbroken fibres, then within this you can also lay fibres on the load paths and structural areas etc. This is the way to do it so you can minimize the amount of expensive carbon fibre you use and also make it stronger and lighter than a solid sheet would be.
If you are up for CNC machining of a sheet material then why not machine a mould to make the part?