Researchers are looking for a better way to treat people who have advanced non-small cell lung cancer (NSCLC) with specific genetic changes called human epidermal growth factor receptor 2 (HER2) mutations. Advanced NSCLC is a group of lung cancers that have spread to nearby tissues or to other parts of the body or that are unlikely to be cured or controlled with currently available treatments. HER2 is a protein that helps cells to grow and divide. A damage (also called mutation) to the building plans (genes) for this protein in cancer cells leads to a production of abnormal HER2 and therefore abnormal cell growth and division. The study treatment, BAY 2927088, is expected to block the mutated HER2 protein which may stop the spread of NSCLC. The main purpose of this study is to learn how well BAY 2927088 works and how safe it is compared with standard treatment, in participants who have advanced NSCLC with specific genetic changes called HER2 mutations. The study participants will receive one of the study treatments: * BAY 2927088 twice every day as a tablet by mouth, or * Standard treatment in cycles of 21 days via infusion (drip) into the vein. The treatment will continue for as long as participants benefit from it without any severe side effects or until they or their doctor decide to stop the treatment. During the study, the doctors and their study team will: * take imaging scans, including CT, PET, MRI, and X-rays, of different parts of the body to study the spread of cancer * check the overall health of the participants by performing tests such as blood and urine tests, and checking * heart health using an electrocardiogram (ECG) * perform pregnancy tests for women * ask the participants questions about how they are feeling and what adverse events they are having. An adverse event is any medical problem that a participant has during a study. Doctors keep track of all adverse events, irrespective if they think it is related or not to the study treatment.