“How then was it counted to him? Was it before or after he had been circumcised? It was not after, but before he was circumcised. He received the sign of circumcision as a seal of the righteousness that he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised, so that righteousness would be counted to them as well,” -Romans 4:10–11
By argument of cause and effect, Paul makes the point then give the purpose for the point.
Paul reasons that if it was counted to Abraham as righteousness (the remission of sins) before he was circumcised, then it corresponds that righteousness was possessed by Abraham before he had been circumcised. Circumcision, then, was a sign of the righteousness he received by faith (when he was still an uncircumcised Gentile).
Why did God order the events this way? It was so Abraham would be the father of all who have faith and not only the father of all them who are circumcised. By being the father of all who have faith, it can be shown that it is by faith that one attains righteousness, not by circumcision.
Although it is not argued here, it was previously mentioned that James’ letter has caused some consternation because it appears that he is contradicting Paul. But, it is clear from Paul’s reasoning that if one were to ask him hypothetically whether some offspring of Abraham who rejected circumcision and refused the rite but claimed he had faith were righteous (had received the remission of sins), Paul would say with James that “faith by itself, if it does not have works, is dead” (James 2:17).
In other words, righteousness is received through faith, but faith, if it is real, will result in works (i.e., circumcision).