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The detection of gravitational waves (GWs) from binary neutron stars (BNSs) with possible telescope follow-ups opens a window to ground-breaking discoveries in the field of multi-messenger astronomy. With the improved sensitivity of current and future GW detectors, more BNS detections are expected in the future. Therefore, enhancing low-latency GW search algorithms to achieve rapid speed, high accuracy, and low computational cost is essential. One innovative solution to reduce latency is the use of machine learning (ML) methods embedded in field-programmable gate arrays (FPGAs). In this work, we present a novel \texttt{WaveNet}-based method, leveraging the state-of-the-art ML model, to produce early-warning alerts for BNS systems. Using simulated GW signals embedded in Gaussian noise from the Advanced LIGO and Advanced Virgo detectors' third observing run (O3) as a proof-of-concept dataset, we demonstrate significant performance improvements. Compared to the current leading ML-based early-warning system, our approach enhances detection accuracy from 66.81\% to 76.22\% at a 1\% false alarm probability. Furthermore, we evaluate the time, energy, and economical cost of our model across CPU, GPU, and FPGA platforms, showcasing its potential for deployment in real-time gravitational wave detection pipelines.