Fermented products are permanently under the attention of scientists and consumers, both due to nutritional importance and health promoting effects. The fermented functional foods contribute to a more balanced diet and increase the immune responses (among many other health effects) with positive implications for quality of life. In this sense, improving the sourdough’s fermentation to boost the biotic (postbiotic and paraprobiotic) properties of the sourdough-based products has positive impacts on the nutritional and functional properties of the final baked products. These enhanced sourdoughs can be obtained in controlled fermentation conditions and used as sourdough bread improvers or novel bioingredients. In this context, our work aimed to optimize, using statistical tools, a gluten-free sourdough based on chickpea, quinoa, and buckwheat fermentation with selected lactic acid bacteria (LAB) to enhance its postbiotic properties. The most important biotechnological parameters were selected by Plackett–Burman Design (PBD) and then Response Surface Methodology (RSM) was applied to evaluate the interactions between the selected factors to maximize the gluten-free sourdough’s properties. As a result, the optimized fermented sourdough had antimicrobial activity with inhibition ratios between 71 and 100% against the Aspergillus niger, Aspergillus flavus, Penicillium spp. molds and against the Bacillus spp endospore-forming Gram-positive rods. The optimized variant showed a total titratable acidity (TTA) of 40.2 mL NaOH 0.1N. Finally, the high-performance liquid chromatography (HPLC) analysis highlighted a heterofermentative profile for the organic acids from the optimized sourdough. Among flavonoids and polyphenols, the level of caffeic and vanillic acids increased after lactic acid fermentation. The comparison between the optimized sourdough and the control evidenced significant differences in the metabolite profiles, thus highlighting its potential postbiotication effect.