A considerable amount of discarded building materials are produced each year worldwide, resulting in ecosystem degradation. Self-compacting concrete (SCC) has 60–70% coarse and fine particles in its composition, so replacing this material with another waste material, such as recycled aggregate (RA), reduces the cost of SCC. This study compares novel Artificial Neural Network algorithm techniques—Levenberg–Marquardt (LM), Bayesian regularization (BR), and Scaled Conjugate Gradient Backpropagation (SCGB)—to estimate the 28-day compressive strength (f’c) of SCC with RA. A total of 515 samples were collected from various published papers, randomly splitting into training, validation, and testing with percentages of 70, 10 and 20. Two statistical indicators, correlation coefficient (R) and mean squared error (MSE), were used to assess the models; the greater the R and lower the MSE, the more accurate the algorithm. The findings demonstrate the higher accuracy of the three models. The best result is achieved by BR (R = 0.91 and MSE = 43.755), while the accuracy of LM is nearly the same (R = 0.90 and MSE = 48.14). LM processes the network in a much shorter time than BR. As a result, LM and BR are the best models in forecasting the 28 days f’c of SCC having RA. The sensitivity analysis showed that cement (28.39%) and water (23.47%) are the most critical variables for predicting the 28-day compressive strength of SCC with RA, while coarse aggregate contributes the least (9.23%).