We present a novel deep Convolutional neural Network (ConvNet)-based approach for coarse Time-of-Arrival (TOA) estimation in Long Range (LoRa)-based Low-Power Wide-Area Networks (LPWANs), overcoming limitations of traditional methods that rely on predefined channel characteristics and synchronization windows. Our approach leverages deep learning to autonomously extract temporal features and complex patterns from received signals, enabling flexible and adaptive TOA estimation. To evaluate the influence of network topology on estimation performance, inference speed, and space complexity, we design and assess four distinct deep ConvNet architectures with varying feature extraction complexities. Simulation results demonstrate that deep ConvNets not only achieve robust TOA estimation across diverse Signal-to-Noise Ratio (SNR) conditions but also highlight the critical influence of network topology on practical deployment factors such as computational efficiency and memory footprint. Furthermore, we propose topology modifications that optimize inference speed and reduce space complexity without compromising estimation accuracy. The proposed solution represents a significant advancement in TOA estimation for LoRa-based LPWANs, offering a scalable and energy-efficient alternative to conventional techniques. Our findings have direct implications for applications requiring wide geographical coverage and low power consumption, such as environmental monitoring and industrial IoT deployments.