Poincaré-free proof of topological rigidity for RCD(0,3) manifolds with Euclidean volume growth

Develop a proof of the statement that any noncollapsed RCD(0,3) topological manifold with Euclidean volume growth is homeomorphic to R^3 that does not rely on Perelman's resolution of the Poincaré conjecture.

Background

Theorem 1.9 establishes that noncollapsed RCD(0,3) manifolds with Euclidean volume growth are homeomorphic to R^3, using the Poincaré conjecture. The authors ask for an alternative approach avoiding Perelman's work, which would provide independent geometric-topological techniques applicable in synthetic settings.

Such a proof would also inform attempts to strengthen biHölder regularity and stability results without relying on deep 3-manifold topology.