The development of sustainable adsorbents is key to addressing the challenges of hydrogen storage in clean energy technologies. In the search for efficient, cost-effective materials with high recovery potential, this research focuses on the synthesis of activated carbons from cork as a sustainable raw material for this application. Two synthesis routes were employed: the first involved a thermochemical pyrolysis process, followed by functionalization with oxalic acid and lithium, and thermal activation in a nitrogen atmosphere at temperatures between 600 and 800 °C. The second route involved hydrothermal carbonization, using a mass ratio (ppm) of oxalic acid to lithium of 2.1:1. Characterization of the materials was carried out using Fourier Transform Infrared Spectroscopy (FTIR), which revealed the presence of functional groups attributed to the synthesis process. Furthermore, Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES) determined that calcium was the predominant element in the original matrix, with a concentration of 1,106 mg/g. Other elements such as potassium (K), magnesium (Mg), and sodium (Na) were also identified as trace elements. The results indicated that the activated carbons with the highest intensity of functional groups were those synthesized under treatment conditions of 0.25 M and 600 °C in the pyrolysis route, and under conditions of 160 °C for 12 hours in the hydrothermal carbonization route. Additionally, a computational chemistry study based on Density Functional Theory (DFT) was conducted using the Perdew-Burke-Ernzerhof (PBE) functional and the def2-SVP basis set to evaluate the interactions between the hydrogen molecule and a graphene sheet with different oxygenated groups.