Applying for MBB whilst starting work at the Big 4

I will be joining a management consulting graduate role at a Big 4 firm this September. I was wondering if I should/would be able to apply for MBB graduate roles (as well as OC&C, Oliver Wyman etc.) in the next recruitment cycle or whether this could potentially burn some ties with the firm I am joining.

I am more interested in a potential strategy consulting role and did receive interviews at some of the above firms last cycle but was unable to progress throughout the rounds. I am therefore uncertain whether or not to complete two years within the firm I am joining and then to evaluate my future options or to apply again for firms in the next recruitment cycle whilst working.