Autonomous flight in unknown environments requires precise spatial and temporal trajectory planning, often involving computationally expensive nonconvex optimization prone to local optima. To overcome these challenges, we present the Neural-Enhanced Trajectory Planner (NEO-Planner), a novel approach that leverages a Neural Network (NN) Planner to provide informed initial values for trajectory optimization. The NN-Planner is trained on a dataset generated by an expert planner using batch sampling, capturing multimodal trajectory solutions. It learns to predict spatial and temporal parameters for trajectories directly from raw sensor observations. NEO-Planner starts optimization from these predictions, accelerating computation speed while maintaining explainability. Furthermore, we introduce a robust online replanning framework that accommodates planning latency for smooth trajectory tracking. Extensive simulations demonstrate that NEO-Planner reduces optimization iterations by 20%, leading to a 26% decrease in computation time compared with pure optimization-based methods. It maintains trajectory quality comparable to baseline approaches and generalizes well to unseen environments. Real-world experiments validate its effectiveness for autonomous drone navigation in cluttered, unknown environments.