Grounding / bonding conductor starts at the service disconnect, goes to the CT (bond) then continues to the ground rod. (grounding)
CT cabinets must be bonded per 250.66 if the conduits are non metalic.
Conductors are frequently paralleled to make it easier to pull. 1,500 KcMil (625 A) or 2x 350 KcMil (2x310A=620A) or 4x 1/0 (4x150A=600A) And to Save Money, and our natural resources.
For a 600 amp service the conductors listed above will all handle the load. Using seperate conduits runs where needed to avoid derating four runs of 1/0 will be a lot less expensive than one run of 1,500 KcMil if you can even find it. Then try to install it.