What could humans do to "see" what dogs smell?
NMR spectroscopy is a technology that is used to identify molecules. So-called "NMR spectra catalogs" document the spectra of various known compounds. Acquiring these spectra requires purified samples, expensive equipment, and time. In addition to making next-generations of this technology into something that would be practical for realtime "smelling", you'd have to match up catalog entries with what dogs actually respond to. That's going to take a fair bit of work.

There's some literature online about growing olfactory sensory neurons in a Petri dish (with difficulty). If we can learn how the signaling pathways work for "odorant detection" for specific odorants or "fragrances" that we already know dogs perceive, perhaps we could genetically engineer a cultured neuron cell to "light up" a fluorescent marker or issue some other signal that is perceptible to humans, whenever some dog-specific odor wafts in. I suspect this would be more realistic than "tabletop NMR" in our lifetime.