The role of electron dynamics in the process of a collisionless shock formation is analyzed with particle-in-cell simulations, the test-particles method, and quasilinear theory. The model of electron stochastic heating in turbulent electromagnetic fields corresponding to the nonlinear stage of two-stream and Weibel instabilities is developed. The analysis of electron and field heating rates shows that the ion motion provides the energy supply for a significant continuous heating of electrons. Such a heating thus plays a role of a friction force for ions, leading to their deceleration and a shock formation.