Recently, BigVGAN has emerged as high-performance speech vocoder. Its sequence-to-sequence-based synthesis, however, prohibits usage in low-latency conversational applications. Our work addresses this shortcoming in three steps. First, we introduce low latency into BigVGAN via implementing causal convolutions, yielding decreased performance. Second, to regain performance, we propose a teacher-student transfer learning scheme to distill the high-delay non-causal BigVGAN into our low-latency causal vocoder. Third, taking advantage of a self-supervised learning (SSL) model, in our case wav2vec 2.0, we align its encoder speech representations extracted from our low-latency causal vocoder to the ground truth ones. In speaker-independent settings, both proposed training schemes notably elevate the performance of our low-latency vocoder, closing up to the original high-delay BigVGAN. At only 21% higher complexity, our best small causal vocoder achieves 3.96 PESQ and 1.25 MCD, excelling even the original small non-causal BigVGAN (3.64 PESQ) by 0.32 PESQ and 0.1 MCD points, respectively.