This study offers a new perspective on the depth-versus-breadth debate in innovation strategy, by modeling inventive search within dynamic collective knowledge systems, and underscoring the importance of timing for technological impact. Using frontier machine learning to project patent citation networks in hyperbolic space, we analyze 4.9 million U.S. patents to examine how search strategies give rise to distinct temporal patterns in impact accumulation. We find that inventions based on deep search, which relies on a specialized understanding of complex recombination structures, drive higher short-term impact through early adoption within specialized communities, but face diminishing returns as innovations become "locked-in" with limited diffusion potential. Conversely, when inventions are grounded in broad search that spans disparate domains, they encounter initial resistance but achieve wider diffusion and greater long-term impact by reaching cognitively diverse audiences. Individual inventions require both depth and breadth for stable impact. Organizations can strategically balance approaches across multiple inventions: using depth to build reliable technological infrastructure while pursuing breadth to expand applications. We advance innovation theory by demonstrating how deep and broad search strategies distinctly shape the timing and trajectory of technological impact, and how individual inventors and organizations can leverage these mechanisms to balance exploitation and exploration.