Myocardial infarction (MI) demands precise and swift diagnosis. Cardiac digital twins (CDTs) have the potential to offer individualized evaluation of cardiac function in a non-invasive manner, making them a promising approach for personalized diagnosis and treatment planning of MI. The inference of accurate myocardial tissue properties is crucial in creating a reliable CDT platform, and particularly in the context of studying MI. In this work, we investigate the feasibility of inferring myocardial tissue properties from the electrocardiogram (ECG), focusing on the development of a comprehensive CDT platform specifically designed for MI. The platform integrates multi-modal data, such as cardiac MRI and ECG, to enhance the accuracy and reliability of the inferred tissue properties. We perform a sensitivity analysis based on computer simulations, systematically exploring the effects of infarct location, size, degree of transmurality, and electrical activity alteration on the simulated QRS complex of ECG, to establish the limits of the approach. We subsequently propose a deep computational model to infer infarct location and distribution from the simulated QRS. The in silico experimental results show that our model can effectively capture the complex relationships between the QRS signals and the corresponding infarct regions, with promising potential for clinical application in the future. The code will be released publicly once the manuscript is accepted for publication.