Reducing the complexity required for starting and maintaining a soliton state has been a major task to fully miniaturize soliton microcombs including the accompanying external operating systems. Here we experimentally examine the generative process of a self-stabilized soliton in which a continuous-wave pump detuned on the thermally stable blue side of a resonance generates a Brillouin lasing signal that relays the pump power to the soliton pulses via intracavity mode-coupling without breaking thermal self-stability. Based on a simple setup consisting of a free-running laser and a microcavity without any external feedback systems by virtue of internal thermal locking, single-soliton pulses of 11 GHz repetition rate were deterministically generated. We demonstrate that the single-soliton pulses can be passively maintained over several days in a laboratory environment with a phase noise performance of -137dBc/Hz at 100 kHz.