Electronic Health Records (EHR) serve as a valuable source of patient information, offering insights into medical histories, treatments, and outcomes. Previous research has developed systems for detecting applicable ICD codes that should be assigned while writing a given EHR document, mainly focusing on discharge summaries written at the end of a hospital stay. In this work, we investigate the potential of predicting these codes for the whole patient stay at different time points during their stay, even before they are officially assigned by clinicians. The development of methods to predict diagnoses and treatments earlier in advance could open opportunities for predictive medicine, such as identifying disease risks sooner, suggesting treatments, and optimizing resource allocation. Our experiments show that predictions regarding final ICD codes can be made already two days after admission and we propose a custom model that improves performance on this early prediction task.