It is not a medicine or cosmetic, just some standard amino acids. I don't see the harm in this particular case as long the ingredients are sold as fit for consumption.
If you don't want to use heat the most straightforward other way to increase the rate of dissolution is to increase the surface area, ie grind it up!
Being that you can see structure with your naked eye the particles are large enough that you should be able to get quite a lot of improvement.
Do you have a coffee grinder?
The solubility will depend on pH for those amino acids that will absorb or release a proton.
I would
guess glutamine is the culprit assuming that your solution is slightly acidic.
This paper has a nice chart of the pH dependence.
http://pac.iupac.org/publications/pac/pdf/1997/pdf/6905x0935.pdf