How do we know God accepts us?

Acceptance by God does not come from our personal righteousness or good works, as the publican in Luke 18 demonstrates. When he prayed for mercy, he recognized his need for a Savior. The only human being ever accepted by God is Jesus Christ, who lived a sinless life. If God imputes Christ's righteousness to us, we are accepted as if we were righteous. Paul writes in Romans that our faith in Jesus' sacrificial death and resurrection is what justifies us before God. Hence, it is not through what we do, but what Christ has done, that we find acceptance.