Catalysts to accelerate foamy polyurethane reaction
In those preparations, the foam arises from the reaction between water and isocyanate, which leads to the production of CO2 via formation of a carbamic acid, which upon decarboxylation generates the blowing agent, CO2.

The trick would be that of making water more reactive towards the isocyanate, without (as expected by a catalyst) partecipating actively in the reaction.

Several compounds of this kind have been reported and are sold, for instance: https://patents.google.com/patent/WO2009048807A2/en mentions N,N,N',N',N",N"-pentaethyldiethylenetriamine and morpholine derivatives, and commercially (I won't link any product, but googling "Blowing Catalysts" might help you) catalysts based on  N-methylmorpholine, Bis[2-(N,N-dimethylamino)ethyl] ether, DMEA and PMDTA are available.

This said, for practical applications the formulations have probably the best ratio of reactants, surfactants and catalyst for obtaining a "good" foam (with good physical properties, and possibly with negligible smell), but if your goal is that of making the reaction go faster, maybe an excess of (any?) tertiary amine, and possibly some drops of water in excess should work in making things faster (with the possible drawback of obtaining a low quality foam, maybe with "bubbles" larger than intended, or with bad "texture").

Additional note: if speed is what you are looking for, gently heating the mixture should work without adding anything else