Enzymes and Digestion
I suspect that the question reveals an incomplete understanding of enzymic catalysis and could more generally be rephrased as "If enzymes just speed up biological reactions, what makes the reactions proceed in the first place." The simple answer to this is the fact that the thermodynamics of the reaction are favourable, i.e. the reaction involves a negative change in (Gibbs) free energy.

So what is stopping the reaction proceeding at a reasonable rate without catalysis? The fact that the thermodynamic path of reactions involves an activated state with a higher free energy. In most cases this is sufficiently large that it acts as a barrier to spontaneous reaction. You can get over the activation barrier by e.g. supplying heat (i.e. supplying activation energy) but this is not possible in living organisms. Enzymes act by lowering the activation energy (energy barrier) or raising the ground state (which in effect decreases the activation energy).

One should realize that "just speeding up the reaction" is generally increasing the reaction rate from being negligible to biologically sufficient. So what makes the reaction go is a combination of the reactants being there with a favourable chemistry and the enzyme being there in the right place to deal with them.

If you are unfamiliar with this basic reaction chemistry see:

http://www.ncbi.nlm.nih.gov/books/NBK22384/#A1100

and the image below from Wikipedia.