This study focused on obtaining an optimal spaghetti-type paste from quinoa flour (60–75%), cassava starch (1.5–5.0%) and water (25–40%) as variable factors and as a fixed egg-white factor (9%). In order to obtain a paste with the highest percentage of protein, the response surface methodology (MSR) with Box–Behnken was used. In addition, the effect of the composition on textural, rheological, and sensory properties was evaluated. Among the most outstanding results, the R2 value indicates that the predictive model explains the 76.33% protein variability. The optimal conditions for quinoa flour, cassava flour, and water were 60%, 1.5%, and 35.28%, respectively. It was shown that the quinoa flour content affects the rheological properties, storage modulus, G', is greater than the loss modulus, G'', in agreement with the maximum breaking force obtained in pasta, indicating behavior more elastic than viscous with good bonding characteristics and dense internal structure. Finally, the application of the experimental design permitted finding the pasta's optimal composition and analyzing the sensory profile by verifying all its attributes; the results obtained indicated that it is possible to prepare a gluten-free pasta with acceptable texture, flavor, and color for the consumer.