L. Cotter, A. Martin-Carrillo, R. A. J. Eyles-Ferris, L. Izzo, D. B. Malesani, Y. Julakanti, G. Corcoran, A. Saccardi, P. G. Jonker, A. J. Levan, F. Carotenuto, P. T. O'Brien, J. H. Gillanders, J. N. D. van Dalen, M. E. Ravasio, S. Schulze, N. Sarin, F. E. Bauer, M. Fraser, J. Quirola-Vasquez, A. P. C. van Hoof, S. J. Smartt, C. Gall, A. Rest, C. T. Murphey, N. Tanvir, T. -W. Chen, S. Campana, C. Ashall, J. P. Anderson, J. A. Chacon, F. J. Cowie, V. D'Elia, L. Galbany, C. P. Gutierrez, D. H. Hartmann, P. Jakobsson, S. Kobayashi, A. H. Kong, P. Mazalli, T. E. Muller-Bravo, M. De Pasquale, L. Rhodes, A. Rossi, J. Sanchez-Sierras, J. Sollerman, A. Andersson, A. Aryan, T. de Boer, J. S. Bright, K. C. Chambers, M. Gromadzki, M. E. Huber, C. Inserra, T. Lowe, P. Minguez, G. S. Narayan, M. Nicholl, G. S. H. Paek, A. Sedgewick, K. W. Smith, J. W. Tweddle, S. Yang

With the advent of the Einstein Probe (EP) mission, we are entering a new era in the study of gamma-ray bursts (GRBs), enabling the detection of faint, low-luminosity transients that would previously have gone undetected. EP250304a was an event discovered by EP associated with the broad-lined type Ic supernova (SN) SN 2025fhm located at z = 0.2. Despite no gamma-ray emission being detected at the time of the EP trigger, we identify evidence for a relativistic outflow consistent with a GRB-like jet across multiple wavelengths. We present a detailed spectral and photometric analysis of EP250304a/SN 2025fhm, including multi-band light curve modelling performed with the Redback Python package. We find that this event closely resembles low-luminosity GRB-SNe (llGRB-SNe) such as GRB 060218/SN 2006aj, GRB 100316D/SN 2010bh, and GRB 171205A/SN 2017iuk, all of which exhibit early-time emission consistent with a thermal shocked cocoon. These similarities suggest that EP250304A/SN 2025fhm may belong to an emerging subclass of shocked cocoon-dominated llGRB-SNe, representing the low-luminosity end of a broader continuum of engine-driven GRB-SN explosions.