Hepatocellular carcinoma (HCC) is a common cancer worldwide and a leading cause of cancer-related death. The majority of participants first presenting with HCC have advanced unresectable or metastatic disease. The purpose of this study is to assess adverse events and how livmoniplimab in combination with budigalimab moves through the body in adult Chinese participants with Locally Advanced or metastatic Child-Pugh A Hepatocellular Carcinoma (HCC). Livmoniplimab is an investigational drug being developed for the treatment of HCC. There are 2 stages to this study. Stage 1 is a safety run-in. There are 2 treatment arms in stage 1 and participants will receive escalating doses of Livmoniplimab in combination with budigalimab (fixed dose). Stage 2 is dose expansion. There are 2 treatment arms in stage 2 and participants will receive Livmoniplimab in combination with budigalimab in multiple doses. Approximately 20 adult participants will be enrolled in the study across 15 sites in China. In part 1 (dose escalation), participants will be intravenously infused with escalating doses of livmoniplimab in combination with budigalimab every 3 weeks. In part 2 (dose expansion), participants will be intravenously infused with livmoniplimab in combination with budigalimab in multiple doses every 3 weeks. The estimated duration of the study is up to 2 years. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic and may require frequent medical assessments, blood tests, and scans.