Venetoclax and Obinutuzumab Followed by Epcoritamab for the Treatment of Untreated Chronic Lymphocytic Leukemia and Small Lymphocytic Lymphoma, LonGEVity Trial

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed or flow cytometry confirmed diagnosis of B-CLL/SLL as documented by medical records and with histology based on criteria established by the World Health Organization (WHO) * No prior treatment for CLL/SLL, except steroids and/or rituximab to treat autoimmune complications * Evidence of CD20 positivity * Active disease meeting criteria for requiring treatment per the International Workshop on Chronic Lymphocytic Leukemia (iwCLL) 2018 guidelines * A minimum of any one of the following constitutional symptoms: * Unintentional weight loss \> 10% within the previous 6 months prior to screening * Extreme fatigue (unable to work or perform usual activities) * Fevers of greater than 100.5°F for ≥ 2 weeks without evidence of infection * Night sweats without evidence of infection * Evidence of progressive marrow failure as manifested by the development of, or worsening of anemia or thrombocytopenia * Massive (i.e., \> 6 cm below the left costal margin), progressive or symptomatic splenomegaly * Massive nodes or clusters (i.e., \> 10 cm in longest diameter) or progressive lymphadenopathy * Progressive lymphocytosis with an increase of \> 50% over a 2-month period, or an anticipated doubling time of less than 6 months * Autoimmune anemia or thrombocytopenia that is poorly responsive to corticosteroids * Symptomatic or functional extranodal involvement (e.g., skin, kidney, lung, spine) * Participant must be able to swallow tablets or capsules. A participant with any gastrointestinal disease that would impair ability to swallow, retain, or absorb drug is not eligible * Without bone marrow involvement: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement. * With bone marrow involvement: ANC ≥ 500/mm\^3 * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement. * Without bone marrow involvement: Platelets ≥ 50,000/mm\^3 * NOTE: independent of transfusion support, with no active bleeding * With bone marrow involvement: Platelets ≥ 30,000/mm\^3 * NOTE: independent of transfusion support, with no active bleeding * Direct bilirubin ≤ 2 x upper limit of normal (ULN) (unless has Gilbert's disease or compensated hemolysis directly attributable to CLL) * Aspartate aminotransferase (AST) ≤ 2.5 x ULN * Alanine aminotransferase (ALT) ≤ 2.5 x ULN * Estimated creatinine clearance of ≥ 40 mL/min using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) 2009 formula * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) ≤ 1.5 x ULN * If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN * If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants * Women of childbearing potential (WOCBP): Negative serum pregnancy test * Agreement by females of childbearing potential to either abstain from heterosexual activity or use an effective method of birth control (failure rate of \< 1% per year) during the treatment period and through at least 30 days after the last dose of venetoclax, 18 months after the last dose of obinutuzumab, 12 months after the last dose of epcoritamab, and at least 4 months after the last dose of tocilizumab (if applicable). Women must refrain from donating eggs during this same period * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) * Examples of contraceptive methods with a failure rate of \< 1% per year include tubal ligation, male sterilization, hormonal implants, established, proper use of combined oral or injected hormonal contraceptives, and certain intrauterine devices * Agreement by males to either abstain from heterosexual activity or use a condom during the treatment period and through at least 30 days after the last dose of venetoclax, 4 months after the last dose of obinutuzumab, epcoritamab or tocilizumab (as applicable). Men with a pregnant partner must agree to remain abstinent or use a condom for the duration of the pregnancy. Men must refrain from donating sperm during this same period Exclusion Criteria: * Chronic use of corticosteroids in excess of 20 mg/day prednisone or equivalent * Major surgery (under general anesthesia) within 30 days prior to cycle 1 day 1 (C1D1) * Uncontrolled coagulopathy or bleeding disorder. Direct oral anticoagulants are allowed * Exposure to vaccination with live vaccine within 30 days prior to C1D1, or anticipated need for such vaccination during treatment * Transformation of CLL to aggressive non-Hodgkin lymphoma (NHL) (Richter's transformation) * Current evidence of central nervous system involvement by the CLL * History of confirmed progressive multifocal leukoencephalopathy (PML) * History of prior malignancy except: * Malignancy treated with curative intent and no known active disease present for ≥ 2 years prior to initiation of therapy on current study * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease * Adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease * Asymptomatic prostate cancer managed with "watch and wait" strategy * Uncontrolled immune hemolysis or thrombocytopenia (positive direct antiglobulin test in absence of hemolysis or history of immune-mediated cytopenias are not exclusions) * Uncontrolled active systemic infection * Known positive test result for hepatitis C (hepatitis C virus \[HCV\] antibody serology testing) and a positive test result for HCV ribonucleic acid (RNA). Participants with positive serology are eligible in case of negative HCV RNA test results * Known positive test result for chronic hepatitis B virus (HBV) infection (defined by hepatitis B virus surface antigen \[HBsAg\] positivity) * Participants with occult or prior HBV infection (defined as negative HBsAg and positive total hepatitis B core antibody) may be included if HBV deoxyribonucleic acid (DNA) is undetectable, provided that they are willing to undergo ongoing DNA testing * Antiviral prophylaxis may be administered as per institutional guidelines * Participants who have protective titers of hepatitis B virus surface antibody (HBsAb) after vaccination or prior but cured hepatitis B may be included if HBV DNA is undetectable * Participants with HIV may be enrolled if they are on concurrent highly active antiretroviral therapy (HAART) therapy, have undetectable HIV RNA levels and no evidence of HIV-related comorbidities (infections or malignancies), and provided that they meet all other protocol-defined eligibility criteria * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)