A challenge of growing interest is how to make topology observable when conventional gap-based frameworks no longer suffice. In bulk-edge correspondence, this challenge arises when the global band gap closes and localized boundary modes disappear, even though the bulk topology remains intact. Here we show that interactions unlock a novel emergent boundary response from this spectrally hidden topology without reopening the global band gap. These interaction-induced excitations originate from a bulk-band minimum, yet reconstruct the characteristic boundary channels of a gapped topological parent sharing the same Bloch eigenspaces. We establish this interaction-enabled bulk-boundary correspondence for first- and higher-order topology in one- and two-dimensional bosonic lattices, respectively, and identify a general compatibility principle governing its emergence. Our results extend bulk-boundary correspondence beyond its conventional spectral manifestation, with experimental prospects in cold-atom and photonic platforms.