Spiking Neural Networks (SNNs) promise significant energy efficiency by processing information via sparse, event-driven spikes. However, realizing this potential is hindered by the conventional use of a rigid, uniform timestep, $T$. This constraint imposes a challenging trade-off between accuracy and latency, while also incurring the prohibitive training costs of Backpropagation Through Time (BPTT). To overcome this limitation, we introduce the Pseudo-Spiking Neuron (PseudoSN), a novel training proxy that conceptualizes latency as an intrinsic, learnable parameter for each neuron. Building on the efficiency of rate-based methods, the PseudoSN models temporal dynamics in a single, BPTT-free pass. It employs a learnable probabilistic noise scheme to emulate the discretization effects of spike generation (e.g., clipping and quantization), making the neuron-specific timestep—and thus latency—directly optimizable via backpropagation. Integrated into a hardware-aware objective, our framework trains heterogeneous-latency SNNs that autonomously learn to optimize the trade-offs among accuracy, latency and energy, establishing a new state-of-the-art on major benchmarks.