A Study to Learn How Safe the Study Treatment Actinium-225-macropa-pelgifatamab (BAY3546828) is, How it Affects the Body, How it Moves Into, Through and Out of the Body, and About Its Anticancer Activity in Participants With Advanced Metastatic Castration-resistant Prostate Cancer (mCRPC)

Researchers are looking for a better way to treat people who have advanced metastatic castration-resistant prostate cancer (mCRPC). In participants with metastatic castration-resistant prostate cancer (mCRPC), the cancer of the prostate has spread to other parts of the body (metastatic) and does not respond to the lowering of testosterone levels in the body (castration resistant). The cancer is 'advanced' and is unlikely to be cured or controlled with currently available treatments. Despite new treatment options for participant(s) with prostate cancer in recent years, the cancer often returns and worsens. The study treatment actinium-225-macropa-pelgifatamab (also called 225Ac-pelgi or BAY3546828) is a new type of treatment under development for participants with mCRPC who have already received available treatments or have few treatment options available. It works by binding to a protein on the surface of the cancer cells called prostate specific membrane antigen (PSMA). As it gives off a type of radioactivity that travels a very short distance, it kills the nearby (cancer) cells that express PSMA. The main purpose of this first-in-human study in participants with mCRPC is to learn: * How safe different doses of 225Ac-pelgi are. * To what degree medical problems caused by 225Ac-pelgi can be tolerated by the participants? * Which dose of 225Ac-pelgi is optimal for treatment (safe and working well)? * How good is 225Ac-pelgi's anticancer activity? To answer this, the researchers will look at: * The number and severity of medical problems that the participants have after treatment with 225Ac-pelgi (per dose level). * The ratio of medical problems and anticancer activity per dose. * Anticancer activity of the optimal 225Ac-pelgi dose as proportion of participants who have at least halved prostate-specific antigen (PSA) levels after 12 weeks of treatment or later and/or shrunken or no longer detectable tumors. * The lowest PSA level reached after treatment start. Doctors keep track of all medical problems (also called adverse events) that participants have during the study, even if they do not think that they might be related to the study treatment. Anticancer activity is measured using cancer imaging techniques and change in blood level of a protein called PSA. PSA is made by normal and by cancerous cells in the body. The PSA level is taken as a marker for prostate cancer development and is usually elevated in participants with mCRPC. In addition, researchers want to find out how 225Ac-pelgi moves into, through and out of the body. The study will have two parts. The first part, called dose escalation, is done to find the most appropriate dose and schedule that can be given in the second part of the study. For this, each participant will receive one of the predefined increasing doses of 225Ac-pelgi as an infusion into the vein. All participants in part 2, called dose expansion, will receive the most appropriate dose and schedule identified from the first part of the study. More than one dose level or schedule from part 1 may be tested. Both the participants and the study team know what treatment the participants will take. Participants in this study will take the study treatment 225Ac-pelgi once in a period of 6 weeks called a cycle. Each participant will have 4 of these treatment cycles, if the participant benefits from the treatment. Each participant will be in the study for up to nearly six years, including a first test (screening) phase of a maximum of 30 days, up to 12 months of treatment depending on the participant's benefit, and a follow-up phase of 60 months after the end of treatment. The following visits to the study site are planned: 2 during the screening phase, 8 in the first treatment cycle, 7 in subsequent cycles, and a visit 6 to 12 weeks after the last dose. In the following 12 months, visits are planned every 6 weeks and during the next 48 months phone calls or clinic visits are planned approximately every 12 weeks. In addition, a sub study during the dose escalation part will gather information on the distribution of the study treatment in the body, the proportion that binds to the cancer cells, and the resulting radiation at the tumor site. During the study, the study team will: * Do physical examinations * Check vital signs such as blood pressure, heart rate, and body temperature * Take blood, and urine samples * Examine heart health using echocardiogram and electrocardiogram (ECG) * Take tumor samples * Track 225Ac-pelgi in the body using gamma imaging (generally available at all study sites) * Check the tumor status using PET (positron emission tomography), CT (computed tomography) or MRI (magnetic resonance imaging) and bone scan * Ask questions about the impact of the disease on the participants' wellbeing and activities of daily life (Eastern Cooperative Oncology Group Performance status (ECOG PS)).