Multi-Agent Path Finding (MAPF) requires collision-free trajectories for multiple agents on a shared graph, often with the objective of minimizing the sum-of-costs (SOC). Many optimal and bounded-suboptimal solvers rely on time-expanded models and centralized conflict resolution, which limits scalability in large or dense instances. We propose a hybrid prioritized framework that separates \emph{geometric planning} from \emph{execution-time conflict resolution}. In the first stage, \emph{Geometric Conflict Preemption (GCP)} plans agents sequentially with A* on the original graph while inflating costs for transitions entering vertices used by higher-priority paths, encouraging spatial detours without explicit time reasoning. In the second stage, a \emph{Decentralized Local Controller (DLC)} executes the geometric paths using per-vertex FIFO authorization queues and inserts wait actions to avoid vertex and edge-swap conflicts. Experiments on standard benchmark maps with up to 1000 agents show that the method scales with an near-linear runtime trend and attains a 100\% success rate on instances satisfying the geometric feasibility assumption. Page of the project: https://sites.google.com/unizar.es/multi-agent-path-finding/home