Silicon nitride (Si3N4) is an ideal candidate for the development of low-loss photonic integrated circuits. However, efficient light coupling between standard optical fibers and Si3N4 chips remains a significant challenge. For vertical grating couplers, the lower index contrast yields a weak grating strength, which translates to long diffractive structures, limiting the coupling performance. In response to the rise of hybrid photonic platforms, the adoption of multi-layer grating arrangements has emerged as a promising strategy to enhance the performance of Si3N4 couplers. In this work, we present the design of high-efficiency surface grating couplers for the Si3N4 platform with an amorphous silicon (α-Si) overlay. The surface grating, fully formed in an α-Si waveguide layer, utilizes subwavelength grating (SWG)-engineered metamaterials, enabling simple realization through single-step patterning. This not only provides an extra degree of freedom for controlling the fiber–chip coupling but also facilitates portability to existing foundry fabrication processes. Using rigorous three-dimensional (3D) finite-difference time-domain (FDTD) simulations, a metamaterial-engineered grating coupler is designed with a coupling efficiency of −1.7 dB at an operating wavelength of 1.31 µm, with a 1 dB bandwidth of 31 nm. Our proposed design presents a novel approach to developing high-efficiency fiber–chip interfaces for the silicon nitride integration platform for a wide range of applications, including datacom and quantum photonics.