We study model near-critical polymer gelling systems made of gluten protein dispersions stabilized at different distances from the gel point. We impose different shear rates and follow the time evolution of the stress. For sufficiently large shear rates, an intermediate stress overshoot is measured before reaching the steady state. We evidence self-similarity of the stress overshoot as a function of the applied shear rate for samples with various distances from the gel point, which is related to the elastic energy stored by the samples, as for dense systems close to the jamming transition. In concordance with the findings for glassy and jammed systems, we also measure that the stress after flow cessation decreases as a power law with time, with a characteristic relaxation time that depends on the shear rate previously imposed. These features revealed in nonlinear rheology could be the signature of a mesoscopic dynamics, which would depend on the extent of gelation.