It can start by itself, or once started it continues by itself without further exertion. Remember rate or speed of reaction is the concern of kinetics. It could be a fraction of a second or 100 years before a measurable amount of products is formed. It is still spontaneous. Natural gas continues to burn once it is lit.
Water runs downhill.
Hydrogen burns in oxygen to form water. Sodium reacts with water. An early criterion for predicting whether or not a process was spontaneous was that it had to exothermic. The sign of H is not enough information to predict accurately whether or not a process is spontaneous. Entropy, symbol is S, is a thermodynamic quantity that is a measure of the randomness or disorder in s system.