The goal of this clinical trial is to observe the efficacy and safety of Sintilimab (a PD-1 inhibitor) combined with Ramucirumab (a VEGFR-2 antagonist) and chemotherapy as a first-line treatment for patients with advanced gastric cancer with liver metastasis.

• Can the combination of Sintilimab, Ramucirumab, and chemotherapy improve the prognosis of patients with AGC and liver metastases?
• What are the adverse events (AEs) associated with the use of the combination regimen of Sintilimab, Ramucirumab, and chemotherapy in patients with AGC and liver metastases?

Participants will:

• Receive a combined treatment regimen of Sintilimab, Ramucirumab, and chemotherapy (SOX (oxaliplatin and S-1) or XELOX (oxaliplatin and capecitabine)), administered every 21 days for up to 6 cycles. Following the completion of 6 cycles, maintenance therapy with Sintilimab and oral chemotherapy agents (capecitabine or S-1) with or without Ramucirumab will be administered until disease progression.
• Imaging assessments will be performed at baseline, after every 2 cycles of treatment, and every 3 months following the completion of 6 cycles of treatment.

Inclusion Criteria:

1. Voluntary participation in the clinical study; full understanding and informed consent to this study by signing the Informed Consent Form (ICF); willingness to follow and ability to complete all trial procedures.
2. Patients with histologically or cytologically confirmed, unresectable, or who refuse surgical resection of locally advanced, recurrent, or metastatic gastric and gastroesophageal junction (GEJ) adenocarcinoma (including signet-ring cell carcinoma, mucinous adenocarcinoma, hepatoid adenocarcinoma, etc.). (Note: For patients who relapse after neoadjuvant/adjuvant therapy, the time from the end of neoadjuvant/adjuvant therapy to disease relapse must be more than 6 months.)
3. Patients, except those with recurrent disease after neoadjuvant/adjuvant therapy, must not have previously received systemic treatment.
4. Participants must be histologically confirmed as having HER2-negative gastric cancer, GEJ cancer, or esophageal adenocarcinoma.
5. There must be at least one measurable lesion in the liver assessed by computed tomography (CT) scan or magnetic resonance imaging (MRI) according to the Response Evaluation Criteria in Solid Tumors (RECIST 1.1) that can undergo repeat radiological evaluation; the radiological tumor assessment should be performed within 28 days prior to randomization.
6. The Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) score of 0-2 within 7 days prior to the first dose of medication.
7. Availability of representative tumor tissue specimens, blood samples, and fecal samples for exploratory research.
8. Main organ functions must be normal, meeting the following criteria:

Liver Function Alanine Aminotransferase (ALT) ≤5.0 × ULN Aspartate Aminotransferase (AST) ≤5.0 × ULN

Exclusion Criteria:

1. History of other active malignancies within the past 5 years or currently having other active malignancies. Treated localized tumors, such as basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, prostate carcinoma in situ, cervical carcinoma in situ, and breast carcinoma in situ, are eligible for inclusion.
2. Underwent surgery within 4 weeks prior to the start of the study treatment.
3. Known history of severe allergy to any monoclonal antibodies or excipients.
4. Previous use of PD-1 inhibitors, LAG-3 inhibitors, CTLA-4 inhibitors, or any other antibodies or drug treatments targeting T-cell co-stimulation or immune checkpoint pathways, including previous receipt of anti-tumor vaccines or other immunostimulatory anti-tumor therapies.
5. Previous exposure to VEGF (vascular endothelial growth factor) or VEGFR inhibitors or any anti-angiogenesis medications.