The purpose of this study is to evaluate the efficacy and safety of AAA617 alone (Lutetium \[177Lu\] vipivotide tetraxetan) and in combination with an Androgen Receptor Pathway Inhibitors (ARPI) in participants with PSMA-positive, castration-resistant prostate cancer and no evidence of metastasis in conventional imaging (CI) (i.e., CT/MRI and bone scans). Approximately 80 participants will be randomized.