We address the question of whether or not assembly bias arises in the absence of highly non-linear effects such as tidal stripping of haloes near larger mass concentrations. Therefore, we use a simplified dynamical scheme where these effects are not modelled. We choose the punctuated Zel'dovich (PZ) approximation, which prevents orbit mixing by coalescing particles coming within a critical distance of each other. A numerical implementation of this approximation is fast, allowing us to run a large number of simulations to study assembly bias. We measure an assembly bias from 60 PZ simulations, each with 5123 cold particles in a 128 h−1 Mpc cubic box. The assembly bias estimated from the correlation functions at separations of ≲ 5 h−1 Mpc for objects (haloes) at z= 0 is comparable to that obtained in full N-body simulations. For masses 4 × 1011h−1 M⊙, the ‘oldest’ 10 per cent haloes are three to five times more correlated than the ‘youngest’ 10 per cent. The bias weakens with increasing mass, also in agreement with full N-body simulations. We find that halo ages are correlated with the dimensionality of the surrounding linear structures as measured by the parameter (λ1+λ2+λ3)/(λ021+λ22+λ23)1/2 where λi is proportional to the eigenvalues of the velocity deformation tensor. Our results suggest that assembly bias may already be encoded in the early stages of the evolution.