The formation of methanol (CH3OH) ice in dense molecular cores may lead to the onset of complex organic molecules, but the conditions promoting its growth is poorly constrained observationally. From laboratory experiments, CH3OH ice can form through the hydrogenation of carbon monoxide (CO) ice on the surface of dust grains, and therefore may form before the birth of a star. To search for early-formation of CH3OH ice, 3-5 micron spectra of stars in the background of small molecular cores reveal both the CH3OH and CO ice features. For the first time it is revealed that CH3OH ice is found in abundance with respect to CO in the pre-stellar phase, showing that the hydrogenation of CO appears to be highly efficient. However, only a small fraction of the lines of sight contain CH3OH ice, presumably only regions with very high local densities of dust and gas. In order to further probe the densities where CH3OH ice forms, maps of the dust extinction in dense cores where CH3OH ice was detected were created using deep infrared images. A new algorithm called AVIATOR implements the inverse Abel transform in order to project the extinction maps into three dimensions. This allows for the measurement of volume densities at any point in the core rather than obtaining only column densities. An initial small sample shows that the total hydrogen densities must be high (>1×105 cm-3) for CH3OH ice to form. I will present how future studies and upcoming JWST observations through our GTO program will further constrain how the local density of dust and gas affects the growth of CH3OH ice and other ices.