Apprenticeship Futures for All Act This bill requires the Office of Apprenticeship within the Department of Labor to award grants, contracts, or cooperative agreements to eligible entities (e.g., program sponsors, training providers, Indian tribes, labor organizations) to (1) support the delivery or expansion of programs under the national apprenticeship system in key sectors identified by the office as targeted for expansion under the system, or for nontraditional apprenticeship populations, women, minorities, individuals with disabilities, and individuals impacted by the criminal or juvenile justice system; or (2) serve programs under the national apprenticeship system in a local or regional setting.