The purpose of this study is to evaluate the efficacy and safety of lutetium (177Lu) vipivotide tetraxetan (AAA617) in participants with oligometastatic prostate cancer (OMPC) progressing after definitive therapy to their primary tumor. The data generated from this study will provide evidence for the treatment of AAA617 in early-stage prostate cancer patients to control recurrent tumor from progressing to fatal metastatic disease while preserving quality of life by delaying treatment with androgen deprivation therapy (ADT).