You mentioned the dam of your mare is out of a Jockey Club mare and a 3/4 TB stallion. I’m assuming that would mean that the 3/4 TB stallion has no proof of pedigree. All of the warmblood registries require proof of four generations of pedigree. ISR/Oldenburg is the only one, I believe, that only requires proof to three generations.
Because of the 3/4 TB stallion back in her pedigree, you would not have proof of pedigree, so your mare could only be entered into the Pre-Mare Book. So unfortunately, no way to get your foal branded and registered Oldenburg.
It can’t be done if the foal has one crossbred parent.
Just a side note that a foal presented to the ISR/Oldenburg registry would only be branded Oldenburg NA. You would have to go with OHBS-GOV in order to get a Oldenburg Verband branded foal. But again, the foal would need to have proof of pedigree going back four generations in order to do that and have Sport Horse approved bloodlines. 