Not a medicinal chemist, but I think the general procedure for that is to do a google (or better, Google Scholar) search for "$chemicalName synthesis".

Here you go:

One-step synthesis of N-acetylcysteine and glutathione derivatives using the Ugi reaction

https://www.sciencedirect.com/science/article/abs/pii/S00404...

I can't seem to find an openly available PDF, but you can search sci-hub to pirate that.

From reading the abstract and the graphics, it doesn't exactly look like something you cook up in the kitchen. For instance they run the reaction in trifluoroethanol, which is flammable, toxic, irritant and possibly causes reduced fertility from exposure.