Is there any code you are aware of that says I MUST install an equipment grounding bar kit in the main service panel/first point of disconnect? Or is it acceptable to use the existing terminal bars that have the grounded neutral supply conductor landed on them from meter with the bonding screw installed for both the branch neutrals and grounding wires? If this makes any sense to you. Thanks
Not unless there is not enough spaces for all the neutrals because you can't put two grounded/neutral conductors in the same hole. Most panel mfg will allow two EGC in one hole but not the grounded conductors. Then you would need to add an extra bar for the EGCs.
Most panels suitable for use as service equipment, will have both bars linked/bonded together, so either bar is fine to land both EGC and grounded conductors.
With that said, if there is any chance the owner might want to add a generator at a later time, it's good practice to have a separate bar for the EGCs.