SN,2025kg, linked to EP250108a, is among the brightest broad-lined Type Ic supernova (SN Ic-BL) known, showing unique helium absorptions, a late-time broad H, and an early bump. In this {\em{Letter}}, we propose a jet-cocoon origin to explain EP250108a as off-axis cooling emission from a mildly relativistic inner cocoon viewed at and the early bump of SN,2025kg as the outer cocoon cooling emission, both constraining an energy of and a progenitor radius of . To explain SN,2025kg’s exceptionally luminous peak, potential energy injection into the ejecta from a magnetar with initial period and magnetic field may be required, implying a rapidly rotating progenitor. Thus, the progenitor may be a low-mass helium star with an extended helium envelope, supported by helium absorption lines and an inferred weak pre-SN wind. Hydrogen-rich material may reside in the inner ejecta layers, as suggested by the late-time broad H, possibly originating from main-sequence companion material evaporated by the magnetar wind. Since the observed near-solar metallicity challenges the popular quasi-chemically homogeneous evolution channel, the rapidly rotating helium-star progenitor of EP250108a/SN,2025kg might attain angular momentum by being tidally spun up by a main-sequence companion in a close binary formed through isolated binary evolution.

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