Nowadays, concretes blended with pozzolanic additives such as fly ash (FA), silica fume (SF), slag, etc., are often used in construction practices. The utilization of pozzolanic additives and industrial by-products in concrete and grouting materials has an important role in reducing the Portland cement usage, the CO2 emissions, and disposal issues. Thus, the goal of the present work is to estimate the compressive strength (CS) of polyethylene terephthalate (PET) and two supplementary cementitious materials (SCMs), namely FA and SF, blended cementitious grouts to produce green mix. For this purpose, five hybrid least-square support vector machine (LSSVM) models were constructed using swarm intelligence algorithms, including particle swarm optimization, grey wolf optimizer, salp swarm algorithm, Harris hawks optimization, and slime mold algorithm. To construct and validate the developed hybrid models, a sum of 156 samples were generated in the lab with varying percentages of PET and SCM. To estimate the CS, five influencing parameters, namely PET, SCM, FLOW, 1-day CS (CS1D), and 7-day CS (CS7D), were considered. The performance of the developed models was assessed in terms of multiple performance indices. Based on the results, the proposed LSSVM-PSO (a hybrid model of LSSVM and particle swarm optimization) was determined to be the best performing model with R2 = 0.9708, RMSE = 0.0424, and total score = 40 in the validation phase. The results of sensitivity analysis demonstrate that all the input parameters substantially impact the 28-day CS (CS28D) of cementitious grouts. Among them, the CS7D has the most significant effect. From the experimental results, it can be deduced that PET/SCM has no detrimental impact on CS28D of cementitious grouts, making PET a viable alternative for generating sustainable and green concrete. In addition, the proposed LSSVM-PSO model can be utilized as a novel alternative for estimating the CS of cementitious grouts, which will aid engineers during the design phase of civil engineering projects.