In the quest for laminar flow control on aircraft wings, quantifying the impact of structural deformation on laminar-turbulent transition remains a challenge. The purpose of this work is to numerically investigate the stability of two-dimensional incompressible boundary layers developing on a flat-plate geometry with indented surfaces of different depths. These surface indentations generate laminar separation bubbles, known to have strong destabilizing effects on Tollmien-Schlichting disturbances. The parallel efficiency of the developed computational tool based on state-of-the-art numerical libraries allows rapid parametric studies within the usually expensive global stability analysis framework. Using an incompressible linearized Navier-Stokes formulation, we use the perfectly matched layer method to absorb waves at the inflow and outflow boundaries. Forced receptivity analysis is performed in order to investigate the effect of the indentation region on the convecting Tollmien-Schlichting waves. Furthermore, the likelihood of global temporal mechanisms arising is investigated through BiGlobal stability analysis. The deepest surface indentation, which features a peak-reversed flow velocity of 9 % in the laminar separation bubble, leads to significant levels of Tollmien-Schlichting amplification. It is also characterized by two temporally unstable modes, namely a dominant, localized stationary mode as well as a traveling Kelvin-Helmholtz mode.