Abstract: Gravitational waves provide a window into the early Universe and a direct probe of the epoch between inflation/reheating and Big Bang nucleosynthesis (BBN), which is otherwise difficult to access. In this talk, I will discuss recent progress towards detecting the cosmological signatures of physics beyond the Standard Model (BSM) at the future space-based interferometer LISA, focusing in particular on gravitational waves associated with cosmic phase transitions in the pre-BBN era. I will highlight open questions and future directions, commenting on other potential sources of gravitational radiation in BSM scenarios and complementarity with collider searches.