We study exact cosmological solutions in f(Q) gravity formulated beyond the coincident gauge, focusing on the non-coincident connection branch ΓB. Using a minisuperspace approach, the field equations are recast into an equivalent scalar-tensor form, enabling analytic reconstruction of cosmological models. We obtain exact solutions of particular interest, including de Sitter, scaling, ΛCDM, Chaplygin gas, generalized Chaplygin gas, and CPL parameterizations. The corresponding scalar potentials and f(Q) functions are derived in closed or parametric form. Our analysis shows that non-coincident f(Q) gravity admits a richer solution space than the coincident case and can describe both early-time inflationary dynamics and late-time acceleration within a unified framework. These results open new directions for testing f(Q) cosmology against observations and exploring its role as a viable alternative to ΛCDM.
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