[Abridged] We combine new CO(1-0) line observations of 24 intermediate redshift galaxies (0.03 < z < 0.28) along with literature data of galaxies at 0<z<4 to explore scaling relations between the dust and gas content using PAH 6.2 $mu$m ($L_{6.2}$), CO ($L_{rm CO}$), and infrared ($L_{rm IR}$) luminosities for a wide range of redshifts and physical environments. Our analysis confirms the existence of a universal $L_{6.2}-L_{rm CO}$ correlation followed by normal star-forming galaxies (SFGs) and starbursts (SBs) at all redshifts. This relation is also followed by local ULIRGs that appear as outliers in the $L_{6.2}-L_{rm IR}$ and $L_{rm IR}-L_{rm CO}$ relations from the sequence defined by normal SFGs. The emerging tight ($sigma approx 0.26$ dex) and linear ($alpha = 1.03$) relation between $L_{6.2}$ and $L_{rm CO}$ indicates a $L_{6.2}$ to molecular gas ($M_{rm H_2}$) conversion factor of $alpha_{6.2} = M_{rm H2}/L_{6.2} = (2.7pm1.3) times alpha_{rm CO}$, where $alpha_{rm CO}$ is the $L_{rm CO}$ to $M_{rm H_2}$ conversion factor. We also find that on galaxy integrated scales, PAH emission is better correlated with cold rather than with warm dust emission, suggesting that PAHs are associated with the diffuse cold dust, which is another proxy for $M_{rm H_2}$. Focusing on normal SFGs among our sample, we employ the dust continuum emission to derive $M_{rm H_2}$ estimates and find a constant $M_{rm H_2}/L_{6.2}$ ratio of $alpha_{6.2} = 12.3 M_{rm H_2}/{rm L}_{odot}$ ($sigmaapprox 0.3$ dex). We propose that the presented $L_{6.2}-L_{rm CO}$ and $L_{6.2}-M_{rm H_2}$ relations will serve as useful tools for the determination of the physical properties of high-$z$ SFGs, for which PAH emission will be routinely detected by the James Webb Space Telescope.
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