She does not intervene directly, but she influences reality in other ways.
First off, Sq’wak is not all powerful, and her nature cannot override the rules that govern reality. But due to her connection with the eternal dishwasher, her essence, her desires, and her thoughts influence the evolution of the universe.
Basically, her existence alters various probabilities of events occurring. For instance, the emergence of certain forms in nature are affected by her existence. Our thoughts are influenced by her existence. Evolution is influenced by her existence.
Unfortunately, because we do not know exactly how everything is influenced, and because we do not have a way to test what the universe would be like without her will being connected to the eternal dishwasher, we cannot test this claim scientifically. We must take it on faith.