Sodium Silicate is basic in solution. It is the salt of a strong base(NaOH) with a weak acid(Silicic, Si(OH)4). You can neutralize it with the HCl. When you do so the lack of available hydroxides and sodiums will cause things to favor silica over silicic and this silica should almost all precipitate... possibly after some time. The goal is to use just a little bit more HCl than is needed to ensure that each Na has a Cl. So initially titrate down to a pH of 6 or so.
When almost all of the silica has precipitated you can measure the pH. Now that the concentration of silicic acid is negligible, any left over acid must just be that portion of hydrochloric which was in excess of what was needed to match the sodium hydroxide. So now knowing the volume and the pH you can just calculate this free hydrochloric fraction and now you have enough information to determine how many sodiums got neutralized.
So now you know the Sodium content of your sample, and of course you also know the original weight of your sample. So you can figure out the sodium oxide weight as a proportion of the total weight of your sample. This is 'fictitious' sodium oxide. It isn't really there as sodium oxide, but this is just how they report the constituents of sodium silicate. They view it as N(Na2O) M(SiO2) Z(H2O), for some N, M and Z.
Now at this stage you do not know the ratio of sodium oxide to silicon oxide. This is the headline ratio that is reported by the manufacturer. However you do know the % Na2O. So you can make the rash assumption that these things tend to dry with the same level of hydration. Take a look at this table:http://www.pqcorp.com/Portals/1/lit/17-2b%20Solid%20Silicates%201-14.pdf
Generally it seems you have about 18% water in the various powders, unless you have an anhydrous powder.
Course that is from just one manufacturer, perhaps it varies afterall.
Anyways since you have solution of known ratio it would be a very good idea to first verify that this method of analysis works on the sample.