The recent direct detection of gravitational waves has highlighted the huge importance of the tensorial modes in any extended gravitational theory. One of the most appealing approaches to extend gravity beyond general relativity is the Eddington-inspired-Born-Infeld gravity which is formulated within the Palatini approach. This theory can avoid the Big Bang singularity in the physical metric although a Big Bang intrinsic to the affine connection is still there, which in addition couples to the tensorial sector and might jeopardize the viability of the model. In this paper, we suggest that a quantum treatment of the affine connection, or equivalently of its compatible metric, is able to rescue the model. We carry out such an analysis and conclude that from a quantum point of view such a Big Bang is unharmful. We expect therefore that the induced tensorial instability, caused by the Big Bang intrinsic to the affine connection, can be neutralized at the quantum level.