In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters1,2. These states can often mimic thermodynamic equilibrium, and a classic example of this is the oscillation threshold of a laser3, which resembles a phase transition in condensed matter. However, many relevant classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity-solitons2 that generally need to be induced by external perturbations, as in the case of optical memories4,5. In the last decade, these highly localised states have enabled significant advancements in microresonator-based optical frequency combs6,7. However, the very advantages that make cavity-solitons attractive for memories – their inability to form spontaneously from noise – have created fundamental challenges. To be reliable sources, microcombs require the essential features of starting laser oscillation naturally, spontaneously and reliably, and of operating in a desired specific state that is intrinsically robust. Largely because of the intrinsic nature of cavity-solitons, these goals have remained elusive8–20. Here, we show that slow nonlinearities of a free-running microresonator-filtered fibre laser21 can transform temporal cavity-solitons into the dominant attractor of the system. This phenomenon leads to reliable self-starting oscillation of (single and multiple) micro cavity-solitons that, in addition, are naturally robust to perturbations, recovering spontaneously even after a complete disruption. These emerge repeatably and controllably into a large region of the global system parameter space, where specific states can be achieved, and which we show are highly stable over long timeframes. These features are all critically needed for the practical implementation of microcombs outside the laboratory.