The health outcomes of increased poverty and inequalities in low- and middle-income countries (LMICs) have been substantially amplified as a consequence of converging multiple crises. Brazil has some of the world's largest conditional cash transfer (Programa Bolsa Família [PBF]), social pension (Beneficio de Prestacão Continuada [BPC]), and primary health care (Estratégia de Saúde da Família [ESF]) programs that could act as mitigating interventions during the current polycrisis era of increasing poverty, slow or contracting economic growth, and conflicts. To evaluate the combined association of the Brazilian conditional cash transfer, social pension, and primary health care programs with the reduction of morbidity and mortality over the last 2 decades and forecast their potential mitigation of the current global polycrisis and beyond. This cohort study used a longitudinal ecological design with multivariable negative binomial regression models (adjusted for relevant socioeconomic, demographic, and health care variables) integrating the retrospective analysis from 2000 to 2019, with dynamic microsimulation models to forecast potential child mortality scenarios up to 2030. Participants included a cohort of 2548 Brazilian municipalities from 2004 to 2019, projected from 2020 to 2030. Data analysis was performed from September 2022 to February 2023. PBF coverage of the target population (those who were poorest) was categorized into 4 levels: low (0%-29.9%), intermediate (30.0%-69.9%), high (70.0%-99.9%), and consolidated (≥100%). ESF coverage was categorized as null (0), low (0.1%-29.9%), intermediate (30.0%-69.9%), and consolidated (70.0%-100%). BPC coverage was categorized by terciles. Age-standardized, all-cause mortality and hospitalization rates calculated for the entire population and by age group (<5 years, 5-29 years, 30-69 years, and ≥70 years). Among the 2548 Brazilian municipalities studied from 2004 to 2019, the mean (SD) age-standardized mortality rate decreased by 16.64% (from 6.73 [1.14] to 5.61 [0.94] deaths per 1000 population). Consolidated coverages of social welfare programs studied were all associated with reductions in overall mortality rates (PBF: rate ratio [RR], 0.95 [95% CI, 0.94-0.96]; ESF: RR, 0.93 [95% CI, 0.93-0.94]; BPC: RR, 0.91 [95% CI, 0.91-0.92]), having all together prevented an estimated 1 462 626 (95% CI, 1 332 128-1 596 924) deaths over the period 2004 to 2019. The results were higher on mortality for the group younger than age 5 years (PBF: RR, 0.87 [95% CI, 0.85-0.90]; ESF: RR, 0.89 [95% CI, 0.87-0.93]; BPC: RR, 0.84 [95% CI, 0.82-0.86]), on mortality for the group aged 70 years and older, and on hospitalizations. Considering a shorter scenario of economic crisis, a mitigation strategy that will increase the coverage of PBF, BPC, and ESF to proportionally cover the newly poor and at-risk individuals was projected to avert 1 305 359 (95% CI, 1 163 659-1 449 256) deaths and 6 593 224 (95% CI, 5 534 591-7 651 327) hospitalizations up to 2030, compared with fiscal austerity scenarios that would reduce the coverage of these interventions. This cohort study's results suggest that combined expansion of conditional cash transfers, social pensions, and primary health care should be considered a viable strategy to mitigate the adverse health outcomes of the current global polycrisis in LMICs, whereas the implementation of fiscal austerity measures could result in large numbers of preventable deaths.