Why is sand that insoluble?
What is Sand?

Scope of this Answer

In order to give a good answer, we first have to decide on the type of sand we want to talk about, because its composition is highly dependent on that. Is it beach sand? If so, where from? All these questions should have been addressed in the question. I will limit the scope of this answer to pure silicium dioxide $\ce{SiO2}$ sand.

Is Sand a Molecule?

Sand is, strictly speaking, not a molecule. It's a crystal. As such it has properties such as the lattice energy. Maybe have a look at that link, it might clarify it all for you already.


So now we have talked about what we want to talk about and clarified the basics, so let's dive right in, shall we?

Why does $\ce{SiO2}$ not Dissolve in Water?

Basically this is an energy calculation. On one hand you have the crystal, with its lattice energy, and on the other hand you have the solvated $\ce{SiO2}$ units. A tentative reaction equation would look like this:
$$ \ce{Si_{n} O_{2n} &lt;&lt;=&gt;[E_\text{lat}] SiO2 &lt;=&gt;[E_\text{solv}] SiO2(aq)} $$

The energies I've indicated are the lattice energy $E_\text{lat} = 12535~\mathrm{kJ\,mol^{-1}}$ (Source) and the solvation energy $E_\text{solv}$ (see figure below, where I've also included sodium chloride as a substance to compare with). 



Data from here (PDF) ($\ce{SiO2}$) and here ($\ce{NaCl}$). It is obvious that the solvation of $\ce{SiO2}$ monomers is highly unfavored (if I got all the sign conventions right, that is...)

Basically, for ease of understanding, imagine that the $\ce{SiO2}$ unit in the middle has to decide on which side it wants to go. Either it forms a crystal with other units (to the left) or it gets solvated by (surrounded by molecules of) water. Which way will it go? We already know that it will take the route to the left. This means that the whole system can release more energy this way. That is why $\ce{SiO2}$ crystals are stable in water. 

Or somewhat. Some theoretical investigations point towards the possibility that the surface of quartz crystals undergo chemisorption of water, thereby generating $\ce{SiOH}$ terminal groups, which would then generate more favorable interactions between the crystal surface and the surrounding water.

Coming back to (a part of) your question:


  Is it because of the big structure that sand makes?


You are kind of on the right track here. It is because of the lower energetical state as a crystal that these big structures (crystals) are formed, vs. the units just being dissolved (solvated by water).