We investigate the sensitivity of low-energy nuclear collisions to intrinsic nuclear structure by studying the interplay between initial-state geometry and final-state observables in C+C and C+Pb collisions at $\sqrt{s_{NN}}=2.36$~GeV, relevant for experiments at the Cooling Storage Ring (CSR) facility in Lanzhou and forthcoming experiments at the High Intensity heavy-ion Accelerator Facility (HIAF) in Huizhou. Calculations are performed within the Jet AA Microscopic Transport Model (JAM) using Woods–Saxon and triangular $\alpha$-clustered configurations for the ${}^{12}C$ nucleus. The initial geometry is characterized in terms of transverse size, compactness, eccentricities, and their ensemble-averaged fluctuations. We find that $\alpha$ clustering leads to a more compact participant configuration than the Woods–Saxon case, while transverse-size and eccentricity fluctuations show only weak sensitivity to clustering. At this beam energy, radial observables remain sensitive to geometric compactness, with the ensemble-averaged proton mean transverse momentum $⟨p_T⟩$ enhanced for the $\alpha$-clustered configuration, whereas pion observables show little sensitivity. The anisotropic response is examined using flow harmonic coefficients. While the flow harmonics and their event-by-event fluctuations exhibit no appreciable differences between the Woods–Saxon and $\alpha$-clustered configurations, normalized symmetric cumulants of the initial-state eccentricities show sensitivity to clustering, whereas the corresponding symmetric cumulants among the final-state flow harmonics do not exhibit a comparably strong separation. These results indicate that the dynamical evolution at $\sqrt{s_{NN}}=2.36$~GeV substantially weakens the imprint of the initial clustered geometry on anisotropic-flow observables, while radial observables remain promising probes of $\alpha$ clustering in low-energy nuclear collisions.