By considering martian-like planetary embryos inside the habitable zone of solar-like stars we study the behavior of the hydrodynamic atmospheric escape of hydrogen for small values of the Jeans escape parameter β<3, near the base of the thermosphere, that is defined as a ratio of the gravitational and thermal energy. Our study is based on a 1-D hydrodynamic upper atmosphere model that calculates the volume heating rate in a hydrogen dominated thermosphere due to the absorption of the stellar soft X-ray and extreme ultraviolet (XUV) flux. We find that when the β value near the mesopause/homopause level exceeds a critical value of ∼2.5, there exists a steady hydrodynamic solution with a smooth transition from subsonic to supersonic flow. For a fixed XUV flux, the escape rate of the upper atmosphere is an increasing function of the temperature at the lower boundary. Our model results indicate a crucial enhancement of the atmospheric escape rate, when the Jeans escape parameter β decreases to this critical value. When β becomes 2.5, there is no stationary hydrodynamic transition from subsonic to supersonic flow. This is the case of a fast non-stationary atmospheric expansion that results in extreme thermal atmospheric escape rates.