When the cement paste is subjected to stresses, the cement matrix and its characteristics are dramatically influenced, especially in the early ages of cement hydration when the cement properties have not yet settled. Nanoclay, which is made up of very small particles, was used to improve the properties of cement. In this study, the early-age performance of cement made with nanoclay powder for use in oil wells is assessed. Ten cement samples were made and cured at varying times (6, 12, 24, 48, and 72 hours), wherein 1% by weight of cement of nanoclay was used in five samples, and in the other five samples, there was no nanoclay present in the cement. Failure properties, petrophysical parameters, and elastic properties were studied for all the cement samples. Nuclear magnetic resonance (NMR), X-ray diffraction (XRD), and scanning electron microscopy (SEM) were all used to describe the cement samples and determine how different curing times affected the cement’s mineralogical and microstructural features. The results displayed that compressive and tensile strengths were shown to increase with curing time for both the base (control) and nanoclay cement samples; however, the compressive and tensile strengths of the nanoclay cement samples were found to be greater than the base sample by 20.2% and 17.9%, respectively. This is due to the presence of more calcium silicate hydrate in these samples. Nanoclay cement had 76.9% lower permeability than control cement, which can be related to the capacity of the nanoclay particles to fill the microstructure dominating the base samples as curing time increased. Young’s modulus of the cement was lowered by 1.8%, while Poisson’s ratio was increased by 2.7% when nanoclay was incorporated. Nanoclay cement has a 29.2% smaller porosity than regular cement, and this porosity increases as the cement cures. The novelty of this work is that several properties of the class G cement were evaluated at the early stage of hydration, where the nanoclay particles were used to improve these properties.