The Lüscher method in Lattice QCD was recently generalized to enable low-energy nuclear scattering results to be extracted from the discrete energy levels of the target-projectile clusters confined by harmonic potential traps. Here we report encouraging results for neutron-$\alpha$ and neutron-$^{24}\mathrm{O}$ elastic scattering from analyzing the trapped levels computed using two different ab initio nuclear structure methods. The $n$-$\alpha$ results have also been checked against a direct ab initio reaction calculation. The $n$-$^{24}\mathrm{O}$ results demonstrate the approach’s applicability for a large range of systems provided their spectra in traps can be computed by ab initio methods. A key ingredient is a rigorous understanding of the errors in the calculated energy levels caused by inevitable Hilbert-space truncations in the ab initio methods.