<jats:p>As the Solar System orbits the Milky Way, it encounters various Galactic environments, including dense regions of the interstellar medium (ISM). These encounters can compress the heliosphere, exposing parts of the Solar System to the ISM while also increasing the influx of interstellar dust into the Solar System and Earth's atmosphere. The discovery of new Galactic structures, such as the Radcliffe wave, raises the question of whether the Sun has encountered any of them. The present study investigates the potential passage of the Solar System through the Radcliffe wave gas structure over the past 30 million years (Myr). We used a sample of 56 high-quality, young (≤30 Myr ) open clusters associated with a region of interest of the Radcliffe wave to trace its motion back and investigate a potential crossing with the Solar System’s past orbit. We find that the Solar System’s trajectory intersected the Radcliffe wave in the Orion region. We have constrained the timing of this event to between 18.2 and 11.5 Myr ago, with the closest approach occurring between 14.8 and 12.4 Myr ago. Notably, this period coincides with the Middle Miocene climate transition on Earth providing an interdisciplinary link with paleoclimatology. The potential impact of the crossing of the Radcliffe wave on the climate on Earth is estimated. This crossing could also lead to anomalies in radionuclide abundances, which is an important research topic in the field of geology and nuclear astrophysics.</jats:p>