Digital twins for cardiac electrophysiology are an enabling technology for precision cardiology. Current forward models are advanced enough to simulate the cardiac electric activity under different pathophysiological conditions and accurately replicate clinical signals like torso electrocardiograms (ECGs). In this work, we address the challenge of matching subject-specific QRS complexes using anatomically accurate, physiologically grounded cardiac digital twins. By fitting the initial conditions of a cardiac propagation model, our non-invasive method predicts activation patterns during sinus rhythm. For the first time, we demonstrate that distinct activation maps can generate identical surface ECGs. To address this non-uniqueness, we introduce a physiological prior based on the distribution of Purkinje-muscle junctions. Additionally, we develop a digital twin ensemble for probabilistic inference of cardiac activation. Our approach marks a significant advancement in the calibration of cardiac digital twins and enhances their credibility for clinical application.