We propose a novel approach to significantly improve the intelligibility in the Non-Audible Murmur (NAM)-to-speech conversion task, leveraging self-supervision and sequence-to-sequence (Seq2Seq) learning techniques. Unlike conventional methods that explicitly record ground-truth speech, our methodology relies on self-supervision and speech-to-speech synthesis to simulate ground-truth speech. Despite utilizing simulated speech, our method surpasses the current state-of-the-art (SOTA) by 29.08% improvement in the Mel-Cepstral Distortion (MCD) metric. Additionally, we present error rates and demonstrate our model's proficiency to synthesize speech in novel voices of interest. Moreover, we present a methodology for augmenting the existing CSTR NAM TIMIT Plus corpus, setting a benchmark with a Word Error Rate (WER) of 42.57% to gauge the intelligibility of the synthesized speech. Speech samples can be found at https://nam2speech.github.io/NAM2Speech/