Visual-inertial odometry (VIO) plays a key role in modern navigation and mapping systems. For their successful integration, an initialization phase, in which IMU-related bias factors are estimated, becomes a fundamental step. Without one, the subsequent nonlinear estimation of the platform pose may fail to converge or completely diverge. As reliance on visual and inertial information may exhibit instability due to error accumulation with time, incorporating absolute positioning information through global navigation satellite system (GNSS) measurements, may enhance its robustness and accuracy. Accordingly, GNSS and visual-inertial initialization frameworks have been receiving growing attention in recent years where current strategies tend to follow a loosely-coupled formulation that first initializes the VIO trajectory, and then aligns it with GNSS measurements. Such strategies are multi-stage, nonlinear, and computationally expensive, motivating us to introduce an alternative framework in which GNSS position is integrated with the raw visual-inertial measurements to form absolute translation constraints. Accordingly, we achieve a closed-form, linear and globally consistent drift-free solution which is computationally efficient and requires neither 3D reconstruction nor nonlinear refinement, as common approaches do. Testing our initialization formulation on benchmark multi-sensor datasets, results show that we outperform current baselines while exhibiting robustness in challenging scenarios.