The unparalleled loss-less electrical current conduction of high-temperature superconducting (HTS) materials encourages research on YBa₂Cu₃O_7−𝛿 (YBCO) to unravel opportunities toward numerous applications. Nonetheless, production costs and throughput of the commercialized HTS Coated Conductors (CCs) are still limiting a worldwide spread. Transient liquid assisted growth (TLAG) is a non-equilibrium process displaying ultrafast growth rate which, when combined with chemical solution deposition (CSD), is emerging as a strong candidate to reduce the cost/performance ratio of YBCO superconductors. This study explores the influence of the (Ba:Cu) molar ratio of the transient liquid composition on the nucleation and growth mechanisms of TLAG. This enables an in-depth analysis of the critical role of the yttrium supersaturation in the transient liquids considering the out-of-equilibrium kinetic character of TLAG. Advanced characterization techniques, including in situ synchrotron X-ray diffraction, coupled to a multi-parameter analysis of the contributions to the physical performance, elucidate the influence of transient liquid supersaturation as driving force toward YBCO nucleation and growth. Understanding the fundamental role played by the initial ink composition allows to disentangle how to reach high superconducting performance. The fabrication of high-performance YBCO films through this novel, high-throughput growth methodology promotes the use of HTS materials in large scale power applications.