When the number of massless fermions exceeds a critical value $N_f^*$, QCD enters the conformal window and becomes chirally symmetric already in the vacuum. Determining $N_f^*$ from lattice simulations is challenging, since calculations are performed at finite lattice spacing, quark mass and temporal lattice size, for which both a thermal transition and an unphysical bulk transition obscure the conformal behaviour. In this work, we present results on the chiral phase boundaries in the bare parameter space $(N_\tau,\;\beta,\;am,\;N_f)$ using unimproved staggered fermions. Our analysis indicates that the chiral transition in continuum QCD is of second order for all $N_f$ up to the onset of the conformal window. By systematically studying the thermal chiral transition and its interplay with the bulk transition, we obtain a coherent picture of the lattice phase structure and suggest how the onset of the conformal window can be identified from simulations performed away from the chiral and continuum limits.