We perform real-time hydrodynamical simulations of the growth of bubbles formed during cosmological first-order phase transitions under the assumption of local thermal equilibrium. We confirm that pure hydrodynamic backreaction can lead to steady-state expansion and that bubble-wall velocity in such case agrees very well with the analytical estimates. However, this is not the generic outcome. Instead, it is much more common to observe runaways, as the early-stage dynamics right after the nucleation allow the bubble walls to achieve supersonic velocities before the heated fluid shell in front of the bubble is formed. This effect is not captured by other methods of calculation of the bubble-wall velocity which assume stationary solutions to exist at all times and would have a crucial impact on the possible generation of both baryon asymmetry and gravitational wave signals.