Just try it

We've all heard the stories of "hmm that's odd" moments, where a discovery is made by someone working on something. Galvanized rubber is the famous example. Note the man had been looking for galvanized rubber for years, it wasn't, as commonly believed, just a freak accident. But the man was there to see it and understand what it meant and test it. How many similar discoveries have passed us by because a farmer didn't see that cotton plant yielding three times the normal amount? Or the housewife didn't take the time to wonder why those three cleaning chemicals left a very hard translucent shell on that one tile which was super easy to clean for ten years? Or the mechanic didn't wonder why what particular pump component which had something spilled on it lasted well beyond its expected end of life?

"Hmm, that's strange" is often enough the mother of discovery, but it doesn't happen frequently enough. This lab would hire a variety of experienced laborers with no science background at all. Their task would be to play with a large number of objects related to their specialty in unusual ways. For example a cook would be tasked with making recipes which definitely should not work for the purpose of finding unusual combinations of ingredients or cooking methods. An electrical engineer would use wires made of mixes of metals that should not improve anything just to see if they do. A worker in plastics would add arbitrary things to batches of plastic to find a kind of plastic which doesn't' act the way it should.

Findings would be investigated by a small team of actual scientists, someone would search through patent history to make sure it wasn't already discovered at some point, the novel idea would be patented, and the patent sold.