Highly efficient nonrelativistic charge-to-spin conversion is a central goal in spintronics. Although exchange-driven spin splitting in altermagnets provides a promising route, the microscopic role of Fermi-surface geometry in controlling spin-channel cancellation and enabling near-unity conversion in two-dimensional (2D) systems remains to be established. Here, we develop a minimal 2D Lieb-type d-wave altermagnetic model that establishes a direct connection between spin-space symmetry, spin-polarized Fermi-surface geometry, and the charge-to-spin conversion efficiency (CSE). The model reveals that nearly flat spin-polarized Fermi-surface segments suppress the cancellation between spin-resolved transport channels, driving the CSE toward unity. Guided by this principle, first-principles transport calculations identify the Cr2O monolayer as an ideal material realization, exhibiting an intrinsic CSE of 92.6% at the charge-neutral point and a maximum CSE of 96.9% at E = EF + 0.03 eV. The conversion remains robust against carrier scattering and is nearly unaffected by spin-orbit coupling, confirming its predominantly exchange-driven origin. These results establish spin-polarized Fermi-surface geometry as a practical design principle for realizing highly efficient nonrelativistic CSE in 2D altermagnets.