First-in-human Study of 225Ac-PSMA-Trillium (BAY 3563254) in Participants With Advanced Metastatic Castration-resistant Prostate Cancer (mCRPC)

Inclusion Criteria: * mCRPC with pathological confirmation of adenocarcinoma without small-cell or neuroendocrine features. * Previous treatment with at least 1 novel androgen axis drug (NAAD) (e.g., enzalutamide, apalutamide, darolutamide and/or abiraterone). * Prior orchiectomy and/or ongoing androgen deprivation therapy and a castrate level of serum testosterone (\<50 ng/dL or \<1.7 nmol/L). * Prior taxane treatment: * Dose Escalation: Participants must either have had prior treatment with at least 1 but no more than 2 taxane regimens, or been deemed ineligible for or refused taxane therapy on consultation with their physician * Dose Expansion Group A: Participants must have had prior treatment with at least 1 but no more than 2 taxane regimens, in the castration-resistant setting * Dose Expansion Group B: Participants must not have received any taxane regimens since becoming castration-resistant * Dose Expansion Group C: Participants must either have had prior treatment with at least 1 but no more than 2 taxane regimens, or been deemed ineligible for or refused taxane therapy on consultation with their physician * Prior treatment with an established Lu-PSMA therapy (i.e., dose activity and cycles comparable to approved treatments) is required for participants in Dose Expansion Group C only. More specifically, to qualify for this expansion group, participants must not have discontinued 177Lu-PSMA treatment due to intolerance. * Eastern Cooperative Oncology Group performance status (ECOG PS) of 0 or 1. * Adequate bone marrow, hepatic, and renal function, as assessed by the following laboratory requirements within 30 days before start of study intervention, as indicated below. Note that blood transfusions (red blood cells or platelets) and administration of G-CSF or GM-CSF are prohibited within 21 days prior to screening for the below bone marrow-related parameters. * Hemoglobin ≥9.0 g/dL * Absolute neutrophil count (ANC) ≥1500/mm\^3 * Platelet count ≥100,000/mm\^3 * Total bilirubin ≤1.5 x the Upper limit of normal (ULN), or ≤3×ULN if the participant has a confirmed history of Gilbert's syndrome (note that participants with Gilbert's syndrome should be carefully evaluated for other liver-related disorders that may impact their suitability for this study). * Alanine transaminase (ALT) and Aspartate transaminase (AST) ˂2.5 x ULN (≤5 x ULN for participants with liver involvement) * Participants on a stable dose of anticoagulation therapy are allowed to participate if they have no sign of bleeding or clotting, and prothrombin time international normalized ratio (PT/INR) and activated partial thromboplastin time (aPTT) test results are acceptable at the Investigator's discretion * Estimated glomerular filtration rate (eGFR) \>60 mL/min/1.73 m\^2, according to the Modified Diet in Renal Disease (MDRD) abbreviated formula and serum creatinine ≤1.5 x ULN * Participants must have at least one PSMA-positive (prostate-specific membrane antigen) distant metastatic lesion on the screening PSMA PET/CT scan using the study-designated PSMA PET tracers, as determined by the site Investigator. For eligibility purposes, a PSMA-positive lesion must have activity greater than the liver by visual assessment of the screening PSMA PET/CT. A PSMA-positive metastatic lesion should not correspond to a normal tissue structure or benign lesion. * Documented progressive mCRPC per PCWG3, and a minimum starting PSA value of 2.0 ng/mL is mandatory. Progressive mCRPC is defined as meeting at least one of the following criteria: 1. PSA progression (defined as 2 consecutive increases over a previous reference value obtained at a minimum of 1-week 2. Radiological progression in soft-tissue lesions according to PCWG3 modification of RECIST v1.1 criteria 3. Progression of bone disease (defined as ≥ 2 new bone lesions according to PCWG3 bone scan criteria) Exclusion Criteria: * Participants who have any of the following tumor lesions which are PSMA negative AND meet the size criteria below are excluded as determined by the site Investigator. A PSMA-negative lesion for eligibility purposes must have activity equal to or less than the liver by visual assessment of the screening PSMA PET/CT scan using the study-designated PSMA PET/CT tracers. A PSMA-negative metastatic lesion should not correspond to a normal tissue structure or benign lesion. * a. Any single or multiple lymph node(s) ≥2.5 cm in the short axis. * b. Any solid organ metastasis (e.g., lung, liver, adrenal glands, etc.) that is ≥1 cm in the short axis. * c. Any bone metastasis with a soft tissue component ≥ 1 cm in short axis with the soft tissue component being PSMA-negative. PSMA-negative osseous metastases without a soft tissue component do not exclude a participant. * d. Predominantly necrotic lesions with greater than 1 cm of enhancing tissue on contrast-enhanced computed tomography / magnetic resonance imaging (CT/MRI). * Prior systemic anticancer therapy including chemotherapy, NAAD, biologic therapy, immunotherapy, or investigational therapies within 4 weeks of the start of study treatment, except luteinizing hormone-releasing hormone (LHRH) or gonadotropin-releasing hormone (GnRH). Start of study treatment is allowed in shorter timeframes if 5 half-lives of the prior drug(s) have elapsed. * Prior radiopharmaceutical treatment using actinium-225. Other prior radiopharmaceutical treatments: * Dose escalation and Dose expansion Groups A and B: Prior treatment with a radiopharmaceutical is prohibited, with the exception of prior treatment with radium-223 dichloride more than 3 months before the start of study intervention. Note: Participants who have discontinued radium-223 dichloride treatment due to intolerance are excluded from Groups A and B. * Dose expansion Group C: Prior treatment with a radiopharmaceutical is prohibited with the following exceptions: Prior treatment with radium-223 dichloride more than 3 mont