The development of technology for integrating optical metaresonators with two-dimensional and layered van der Waals (vdW) materials opens up broad prospects for the creation of subdiffraction concentrators of electromagnetic energy, surface-emitting lasers, laser displays, and highly efficient nonlinear converters. In this work, we develop a straightforward strategy for the design and fabrication of surface-emitting laser devices based on few-layer transition metal dichalcogenides placed on the dielectric metasurfaces in the regime of quasi-trapped mode excitation. We optimize the parameters of MoTe2 flake and Si metasurface to achieve a positive feedback and to observe the lasing, resulting from their integration, with the predicted characteristics. Promising potential for the development of vdW-metalaser platform is associated with the possibility of simple polarization control of lasing regimes by employing the features of the bianisotropic response of the metasurface's building blocks.