Yup, through Christ. But who is Christ? He is both part and the whole of the Trinity incarnate: Fully man, but also fully God, Himself, and the Holy Spirit.
So a promise by God in the Old Covenant is a promise by Christ. What, He wasn’t born yet? Irrelevant, for Christ is fully God and therefor the Alpha and Omega (in our terms, the start and end, outside of time).
And those OT followers were those who, like Abraham, “believed” and it was “counted to them as righteousness”.
Having said that, Christ came to fulfill the law. There is no alternate route to Heaven for Jews or anyone else - only faith in Him. One cannot reject His son and gain Heaven because one has done good works, lived a good life, has membership in a specific religion/denomination, whatever.