Large language models (LLMs) have shown strong capabilities in software engineering tasks, yet most existing LLM-based SWE-Agents mainly tackle well-defined problems using conventional methods, often overlooking alternative or innovative solutions beyond their predefined frameworks. This limitation is evident in open-world software environments, where emerging challenges transcend established paradigms. We propose U2F (Unknown Unknowns to Functional solutions), a cognitive-inspired, uncertainty-embracing multi-agent framework that systematically surfaces "Unknown Unknowns" - novel solution pathways absent from initial formulations but holding innovative potential. U2F consists of two key components: (1) a Discovery-Exploration-Integration agent system for uncovering and synthesizing potential solutions, and (2) cognitive enhancement mechanisms across three dimensions: cross-domain analogical reasoning, reverse thinking, and external validation, which strategically reframe and extend conventional solution boundaries. Applied to 218 real-world software enabler stories curated from authentic engineering tasks, U2F achieved notable improvements: human experts reported a 14 percent increase in overall novelty, 51 percent improvement in semantic novelty, and stable feasibility (4.02/5.0), corroborated by an LLM-based evaluator. These results highlight the potential of embracing uncertainty as a catalyst for innovation in software engineering.