The Purkinje tree plays a determinant role in the activation sequence of the human heart. Alterations in the structure of this tree and myocardial conduction properties can serve as a substrate for lethal ventricular arrhythmias. However, these activation properties cannot be measured from standard clinical tests. Recent studies have demonstrated cardiac digital twins using inference methods integrating cardiac magnetic resonance (CMR) imaging and electrocardiogram (ECG) data. Sophisticated strategies to physiologically constraint the Purkinje structure in these cardiac digital twins would augment standard clinical data to inform Purkinje related risk-stratification. This study presents and evaluates new computational techniques to infer physiological earliest biventricular activation sites and cardiac conduction properties from clinical CMR and ECG using Eikonal simulations. We extend our sequential Monte Carlo approximate Bayesian computation-based inference method to clinical 12-lead ECGs and incorporate a pseudo-Purkinje strategy to generate physiologically sound earliest activation sites. We demonstrate our inference and Purkinje reconstruction methods on a clinical subject with a cardiac ventricular myocardial-mass volume of 171 cm3.