Building a universal multilingual automatic speech recognition (ASR) model that performs equitably across languages has long been a challenge due to its inherent difficulties. To address this task we introduce a Language-Agnostic Multilingual ASR pipeline through orthography Unification and language-specific Transliteration (LAMA-UT). LAMA-UT operates without any language-specific modules while matching the performance of state-of-the-art models trained on a minimal amount of data. Our pipeline consists of two key steps. First, we utilize a universal transcription generator to unify orthographic features into Romanized form and capture common phonetic characteristics across diverse languages. Second, we utilize a universal converter to transform these universal transcriptions into language-specific ones. In experiments, we demonstrate the effectiveness of our proposed method leveraging universal transcriptions for massively multilingual ASR. Our pipeline achieves a relative error reduction rate of 45% when compared to Whisper and performs comparably to MMS, despite being trained on only 0.1% of Whisper's training data. Furthermore, our pipeline does not rely on any language-specific modules. However, it performs on par with zero-shot ASR approaches which utilize additional language-specific lexicons and language models. We expect this framework to serve as a cornerstone for flexible multilingual ASR systems that are generalizable even to unseen languages.