The synthesis of substituted 2,4,6,8,10,12-hexaazaisowurtzitane via direct condensation is challenging. The selection of starting ammonia derivatives is very limited. The important step in developing alternative synthetic routes to these compounds is to investigate their formation process in detail. Here, we examined an acid-catalyzed condensation between benzyl carbamate and glyoxal in a ratio of 2:1 in a range of polar protic and aprotic solvents, and discovered a new process occurring during the cascade condensation of glyoxal with ammonia derivatives as well as discovered several processes hindering the formation of caged compounds. More specifically, a cyclic compound, N,N'-bis(carbobenzoxy)-3,6-diamino-1,4-dioxane-2,5-diol, was found to form at the early stage of condensation under low acidity conditions. The formation of this compound is governed by an easier condensation of alcohol groups compared to the amide ones. The condensation intermediates, N,N'-bis(carbobenzoxy)ethan-1,2-diol, N,N',N″-tris(carbobenzoxy)ethanol, and N,N',N″,N‴-tetrakis(carbobenzoxy)ethan, were obtained at a higher acidity. A range of solvents were identified: those that react with benzyl carbamate, those that promote the progress of side processes, and those that promote precipitation of condensation intermediates. A few byproducts were isolated and identified. It was found that DMSO exhibits a strong deactivating ability, while CH3CN exhibits a strong activating ability towards the acid-catalyzed condensation process of benzyl carbamate with glyoxal.