Most commentaries (and many translations) say that “According the flesh” means our “earthly father” or “the father or our race”, or “physical ancestor”. The greek works for flesh “sarx” is translated as “countrymen” or “fellow jews” in Romans 11:4.
For Instance The HCSB says: What then can we say that Abraham, our physical ancestor, has found?
The NLT says: Abraham was, humanly speaking, the founder of our Jewish nation. What did he discover about being made right with God?
Also, keep in mind that there was no true Mosaic Law at the time of Abraham. There was no Passover, no Temple, no festivals or feast or fast…
This is referring to life under the old law. Romans 2 all the way to Romans 3:20 described how both the Jews and the Gentiles were judged under the old covenant. So Romans 2:13 is a true statement if you are following the Jewish law or were a Gentile following the moral/nature law. The only hope is to follow the law exactly and never sin. James 2:10 says For whoever keeps the whole law but fails in one point has become guilty of all of it.
That is why in Romans 3:20 Paul says, For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.
If you just pull out those two verses from Romans it is easy to think Paul is contradicting himself. Does keeping the law justify us or not? To answer this question you have to read 3:9. What then? Are we Jews any better off? No, not at all. For we have already charged that all, both Jews and Greeks, are under sin,
Having the Jewish law didn’t make the Jews any better than the gentiles because they are both under sin. Neither of them were sinless. Neither of them were perfect doers of the law (either Mosaic or moral) which is why "by the works of the law no human being will be justified in his sight"
That is a very hopeless situation to be in and it is the situation we are all born into. If the only way to gain eternal life is to follow the law exactly and any sin is breaking the law then what hope do I have? If this is the case then no human being ever could be justified in his sight because we are all sinners.
This is when Paul says, perhaps the two most beautiful words in his letter.
But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— 22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: 23 for all have sinned and fall short of the glory of God, 24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a propitiation by his blood, to be received by faith.