Large language models (LLMs) have demonstrated strong reasoning ability when given additional compute at inference time. However, existing inference-time scaling methods are fundamentally limited by their design. On the one hand, goal-oriented approaches, such as Line or Tree Search, refine candidate solutions using previous feedback but are vulnerable to sequential dependence, often collapsing into suboptimal reasoning trajectories. On the other hand, process-oriented approaches such as Best-of-N sampling encourage diversity through random exploration but lack feedback mechanisms, leading to inefficient computation allocation and unguided search. In this work, we propose EvoMo, a novel inference-time scaling approach that unifies both paradigms by embedding a globally evolving strategy pool into MCTS, where each node expansion selects reasoning strategies under an -soft policy. To further avoid stagnation in familiar strategies, we introduce a momentum-based optimization mechanism that monitors similarity among generated solutions and encourages the exploration of underutilized strategies. We also present a theoretical analysis of the effectiveness of the proposed momentum mechanism by modeling it as a self-evolving pool of actions. Across benchmarks, EvoMo reveals significant performance gains over SOTA inference scaling methods. We observe competitive performance, like in APPS and CodeContests, with up to a 4.5% and 3.63% relative gain in Pass@K compared to the leading baseline within 40 search-budget, highlighting the potential of hybrid evolutionary search as a general paradigm for test-time scaling.