Being declared righteous by faith comes with hope: the hope of being resurrected and glorified when Christ returns. We need not try to be made perfect by the flesh (the works of the law) (Gal 3:2-3). We began in the Spirit by faith; now we wait through the Spirit by faith, at no time resorting to the works of the law (the flesh) to be perfected. In short, the righteousness we have by faith is already perfect; we received the Spirit through faith, we walk in the Spirit through faith, and through the Spirit, we wait right in here in the righteousness we already have by faith, that we may be found in Him, not having our own righteousness, but the righteousness which is of God by faith.
Compare Galatians 3:2-3 with Galatians 5:4-5 and also Philippians 3:3-9 and this should be much more clear.
Bottom line, we're not waiting for righteousness; we're waiting for the fruits of the righteousness we've already been given. We have the firstfruits now, and as we wait through the Spirit rather than striving through the flesh, we will be found in Him and obtain what it is we are hoping for.
The whole book of Galatians is a command to continue in the Spirit, which means continuing to boast/rejoice/glory only in Christ and the Cross and having no confidence in the flesh (any means of righteousness other than the cross)(Gal 3:2-3, 6:14, Phi 3:3-9).
Notice how the phrase "hope of" is used here:
"In the body of His flesh through death, to present you holy and unblameable and unreproveable in His sight: If ye continue in the faith grounded and settled, and be not moved away from the hope of the Gospel, which ye have heard, and which was preached to every creature which is under heaven; whereof I Paul am made a minister;" Colossians 1:22-23
The hope of the Gospel does not refer to waiting for the Gospel. It's waiting to be presented holy and unblameable and unreproveable in His sight, which is the result of being not moved away from the Gospel. In Colossians 1:22-23, Paul is actually saying the exact same thing he's saying in Galatians 5:5. Don't be moved away from the faith by resorting back to the works of the law. Continue in the faith, rest in the righteousness you've already been given, and you will eventually be presented holy in God's sight.
You were declared righteous when you died to the law by the body of Christ. When this happened, you received the Spirit of Life (as Life only comes through death) and the Spirit began perfecting you. Rest there in that perfect righteousness, rely on your having been crucified with Christ and having received Christ in you, the hope of glory, and you will one day receive the hope of righteousness: being fully conformed into the image of Christ (1 John 3:2, 1 Cor 13:12, 2 Cor 3:18, Rom 8:24,29).