Neoadjuvant Atezolizumab-Based Combination Therapy in Men With Localized Prostate Cancer Prior to Radical Prostatectomy

Inclusion Criteria: 1. Histologically confirmed adenocarcinoma of the prostate. a. Subjects with small cell or neuroendocrine PC are not eligible. 2. Eligible for radical prostatectomy as determined by urologic oncology surgeon, and subject consents to proceeding with radical prostatectomy. a. Deemed by urologic oncology surgeon to be appropriate for a "window-of-opportunity"study. 3. Only patients with high-risk disease are eligible for the safety lead-in for each cohort. Patients with intermediate-risk disease will be included after interim analyses is complete for the corresponding cohort and the PI has determined that it is safe to do so. 4. Availability of a representative tumor specimen that is suitable for the planned study analyses, as determined by the Principal Investigator. 1. A formalin-fixed paraffin-embedded (FFPE) tumor specimen in a paraffin block (preferred) or at least 15 slides containing unstained, freshly cut, serial sections should be submitted along with an associated pathology report prior to study treatment. If only 10-14 slides are available, the patient may still be eligible for the study, after Principal Investigator approval has been obtained. 2. If archival tumor tissue is unavailable or is determined to be unsuitable for required testing, tumor tissue must be obtained from a biopsy performed at screening. Refer to Section 6.3 for additional information on tumor specimens collected at screening. 5. Subjects have not received any prior systemic or locally directed therapy for PC (see exclusion criteria). 6. Age \>= 18 years 7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 8. Requirements for organ and marrow function: * Hemoglobin \>= 9 g/dL * \- Participants must not have been transfused within 2 weeks prior to screening to meet this criterion * Absolute neutrophil count \>= 1,500/microliter (uL) without granulocyte colonystimulating factor support * Absolute lymphocyte count \>= 500/uL * Platelets \>= 100,000/uL without transfusion * Total bilirubin \< 1.5 x institutional upper limit of normal (ULN) (known Gilbert disease: \< 3 x ULN) * Alkaline phosphatase \< 2 x institutional ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT)) =\< 2 x institutional ULN * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =\< 2 x institutional ULN * International normalized ratio (INR) or activated partial thromboplastin time (aPTT) \< 1.5 x institutional ULN for subjects not receiving therapeutic anticoagulation * Creatinine clearance \>= 30 mL/min (calculated using the Cockcroft-Gault formula) * Serum creatinine \<=1.6 mg/dL (141 μmol/L) in female patients and ≤1.9 mg/dL (168 μmol/L) in male patients . Patients with serum creatinine values exceeding limits may be eligible for the study if their estimated glomerular filtration rates (GFR) are \>30 9. Testosterone level \> 150 ng/dL. 10. Contraception: agreement to remain abstinent or use contraceptive measures, and agreement to refrain from donating sperm as defined below: 1. With female partners of childbearing potential: men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for 4 months after the last dose of study treatment. Men must refrain from donating sperm during the same period 2. With pregnant female partners: men must remain abstinent or use a condom during the treatment period and for 4 months after the last dose of study treatment to avoid exposing the embryo 3. Abstinence: the reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception 11. For patients receiving therapeutic anticoagulation: stable anticoagulant regimen \> 3 months. 12. Ability to understand a written informed consent document, and the willingness to sign it. 13. Ability to comply with the study protocol, in the investigator's judgment. Exclusion Criteria: 1. Evidence of metastatic disease as determined by standard staging scans. a. Staging scans should be performed per urologic standard of care for patients undergoing radical prostatectomy \[per American Urological Association (AUA)/National Comprehensive Cancer Network (NCCN) guidelines\]. 2. Not a candidate for radical prostatectomy as determined by treating urologic oncology surgeon. 3. Any prior systemic therapy for PC, including antiandrogens, androgen deprivation therapy \[gonadotropin-releasing hormone (GnRH) agonist or antagonist\], chemotherapy, targeted therapy, immunotherapy, OR radiopharmaceuticals. a. Subjects who are on finasteride or dutasteride must discontinue therapy and undergo a washout period of 6 weeks to become eligible for the study. Screening procedures should begin following the washout period. 4. Prior radiotherapy for PC. 5. Any history of prior malignancy, except: 1. Non-melanoma skin cancer treated with curative intent 2. Carcinoma-in-situ (CIS) treated with curative intent, without evidence of recurrence or disease progression for 3 years 3. Appropriately treated Stage I uterine cancer 4. All other cancer: treated with curative intent and without evidence of disease on standard of care follow-up for 5 years 6. 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, Sjogren's syndrome, Guillain-Barre syndrome, or multiple sclerosis, with the following exceptions: 1. Subjects with a history of autoimmune-re