Inclusion Criteria:  Written informed consent in accordance with federal, local, and institutional guidelines. Participants must provide informed consent prior to the first screening procedure. Ability to comply with the study protocol, in the investigator's judgment. Locally advanced or metastatic and/or unresectable Hepatocellular Carcinoma (HCC) with diagnosis confirmed by histology/cytology or clinically by American Association for the Study of Liver Diseases (AASLD) criteria in cirrhotic patients. Participants without cirrhosis require histological confirmation of diagnosis. Disease that is not amenable to curative surgical and/or locoregional therapies, or progressive disease after surgical and/or locoregional therapies. No prior anti-neoplastic systemic therapy (including systemic investigational agents) for HCC At least 1 measurable (per RECIST v1.1) untreated lesion. Participants who received prior local therapy (e.g., radiofrequency ablation, percutaneous ethanol or acetic acid injection, cryoablation, high-intensity focused ultrasound, transarterial chemoembolization, transarterial embolization, etc.) are eligible provided the target lesion(s) have not been previously treated with local therapy or the target lesion(s) within the field of local therapy have subsequently progressed in accordance with RECIST version 1.1. Participants must undergo an esophagogastroduodenoscopy (EGD), and all size of varices (small to large) must be assessed and treated per local standard of care prior to enrollment. Participants who have undergone an EGD within 6 months of prior to initiation of study treatment do not need to repeat the procedure. Eastern Cooperative Oncology Group (ECOG ) Performance Status (PS) of ≤ 2 Participants with brain metastases must have treated and stable brain metastases. Child-Pugh Class A within 7 days prior to Cycle 1 Day 1. Adequate hepatic function at screening Adequate renal function within 28 days prior to cycle 1 day 1 Adequate hematopoietic function within 7 days prior to cycle 1 day 1 Urine dipstick for proteinuria <2+ (within 28 days of cycle 1 day 1. Patients discovered to have ≥ 2+ proteinuria on dipstick urinalysis at baseline should undergo a 24-hour urine collection and must demonstrate < 1 g of protein in 24 hours. No known history of human immunodeficiency virus. Documented virology status of hepatitis, as confirmed by screening HBV and HCV serology test. For patients with active hepatitis B virus (HBV): HBV DNA ≤ 500 IU/mL obtained within 28 days prior to initiation of study treatment, and Anti-HBV treatment (per local standard of care, e.g., entecavir) for a minimum of 14 days prior to study entry and willingness to continue treatment for the length of the study Female participants of childbearing potential must agree to use 2 methods of contraception (including 1 highly effective and 1 effective method of contraception) and have a negative serum pregnancy test at Screening. Male participants must use an effective barrier method of contraception if sexually active with a female of childbearing potential. For both male and female participants, effective methods of contraception must be used throughout the study and for 6 months following the last dose of study treatment. Women of childbearing potential must have a negative serum pregnancy test result within 14 days prior to initiation of study treatment.  Exclusion Criteria:  History of leptomeningeal disease  Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain Barré syndrome, or multiple sclerosis, with the following exceptions:  Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study. Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: (a) Rash must cover ≤ 10% of body surface area (b) Disease is well controlled at baseline and requires only low-potency topical corticosteroids (c) No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months Prior exposure to a SINE compound, including SELINEXOR. History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted. Known active tuberculosis Significant cardiovascular disease (such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident within 3 months prior to initiation of study treatment), unstable arrhythmia, or unstable angina History of congenital long QT syndrome or corrected QT interval >500msec (calculated with use of the Fridericia method) at screening Prior allogeneic stem cell or solid organ transplantation Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that contraindicates the use of an investigational drug, may affect the interpretation of the results, or may render the patient at high risk from treatment complications Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment, or anticipation of need for such a vaccine during atezolizumab treatment or within 5 months after the last dose of atezolizumab History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC Untreated or incompletely treated esophageal and/or gastric varices with bleeding or high risk for bleeding. A prior bleeding event due to esophageal and/or gastric varices within 6 months prior to initiation of study treatment Co-infection of HBV and hepatitis C virus (HCV). Participants with a history of HCV infection but who are negative for HCV RNA by polymerase chain reaction (PCR) will be considered non-infected with HCV. Uncontrolled tumor-related pain, symptomatic hypercalcemia (ionized calcium >1.5 mmol/L, calcium >12 mg/dL or corrected serum calcium > ULN); pleural effusion, pericardial effusion or ascites requiring recurrent drainage procedures. Participants with indwelling catheters are allowed. Treatment with investigational therapy within 28 days prior to initiation of study treatment Treatment with strong CYP3A4 inducers within 14 days prior to initiation of study treatment, including rifampin (and its analogues) or St. John's wort Prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA-4, anti PD-1, and anti-PD-L1 therapeutic antibodies Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and interleukin 2 [IL-2]) within 4 weeks or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, an anti-Tumor Necrosis Factor [TNF] -α agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment, with the following exceptions: If patient is on chronic steroid prednisone equivalent less than 15 mg/day are allowed. Inadequately controlled arterial hypertension (defined as systolic blood pressure (BP) ≥ 150 mmHg and/or diastolic blood pressure ≥ 100 mmHg), based on an average of ≥ 3 BP readings on ≥ 2 sessions. Anti hypertensive therapy to achieve these parameters is allowable. Significant vascular disease (e.g., aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to initiation of study treatment History of life-threatening bleeding within 3 months of C1D1, bleeding diathesis or significant coagulopathy. Current or recent (within 10 days of first dose of study treatment) use of anti-platelet treatment, full-dose oral or parenteral anticoagulants or thrombolytic agents for therapeutic (as opposed to prophylactic) purpose History of abdominal or tracheoesophageal fistula, gastrointestinal (GI) perforation, or intra-abdominal abscess within 6 months prior to initiation of study treatment History of intestinal obstruction and/or clinical signs or symptoms of GI obstruction including sub-occlusive disease related to the underlying disease or requirement for routine parenteral hydration, parenteral nutrition, or tube feeding prior to initiation of study treatment Serious, non-healing or dehiscing wound, active ulcer, or untreated bone fracture Metastatic disease that involves major airways or blood vessels, or centrally located mediastinal tumor masses (< 30 mm from the carina) of large volume Participants with vascular invasion of the portal or hepatic veins may be enrolled. Radiotherapy, local therapy to the liver or major surgical procedure within 28 days of C1D1 of treatment. Chronic daily treatment with a nonsteroidal anti-inflammatory drug (NSAID). Occasional use of NSAIDs for the symptomatic relief of medical conditions such as headache or fever is allowed. Any active gastrointestinal dysfunction interfering with the patient's ability to swallow tablets, or any active gastrointestinal dysfunction that could interfere with absorption of study treatment.