Since God is pure, living out our faith as worship before him (Romans 12:1,2) is also to be pure:
Religion that is pure and undefiled before him is this: to visit orphans and widows in their affliction, and to keep oneself unstained by the world. [1:27]
Who shall ascend the hill of the LORD? And who shall stand in his holy place? He who has clean hands and a pure heart, who does not lift us his soul to what is false, and does not swear deceitfully. [Psalm 24:3,4]
As believers in Christ who live lives in worship to him, we are called to be holy as he is holy (Matthew 5:48; 1 Peter 1:15,16). Like it is with wisdom, we also lack holiness. Jesus prayed for us as believers regarding this (John 17:17). Our sanctification (making us holy, conforming us to the image of Christ) is what God (Father, Son and Holy Spirit) is accomplishing as we live out our faith here until Christ returns. Remembering that he does this individually for each of us as part of the body of Christ (Ephesians 4:1-16), and for his church as a whole (Ephesians 5:25-27). James implies this when he writes with terms such as my brothers and among you. Knowing that it is God, who is holy, who works in us to will and to act according to his good purpose is why we are to work out our own salvation in fear and trembling (Philippians 2:12, 13). That he works this through his word by his Holy Spirit reminds us and teaches us to be in his word which is pure (Psalm 19:7-9).
What does scripture teach about how God works through his wisdom which is first pure? And how are we to work in response with the wisdom he gives?
In Christ, who is to us wisdom from God (1 Corinthians 1:30), he justifies us and sanctifies us and will one day glorify us and through his word by his Holy Spirit. The holiness of the wisdom of God is necessary in producing the righteousness of God – his work and our work in response to his working:
Proverbs 2 and 3; Romans 4:20-26; Romans 5:1-5; Ephesians 2:10, 21; Philippians 2:12-16; Colossians 1:9-12; Colossians 3:1-17; Titus 1:15-2:14; James 1:19-21.
In his holiness, God is above all working for his glory. That he himself is first pure, then peaceable towards those whom he has favored and blessed is to his glory alone.
What are we to do in light of his holiness and his peace (his grace) toward us?
Consider the words of our Lord and Savior Jesus Christ, the son of God:
You are the light of the world. A city set on a hill cannot be hidden. Nor do people light a lamp and put it under a basket, but on a stand, and gives light to all in the house. In the same way, let your light so shine before others, so that they may see your good works and give glory to your Father who is in heaven. [Matthew 5:14-16]
And the psalmist by the Holy Spirit:
Not to us, O LORD, not to us but to your name give glory. [Psalm 115:1]
It is only in the meekness of wisdom that we can say this. Remember the context of where we are in James and the question being asked: Who is wise and understanding among you? By his good conduct (by his speech), let him show his good works in the meekness of wisdom.
And that we can pray as Jesus taught us to pray:
Our Father in heaven, hallowed be your name… [Matthew 6:9-13]
And study and obey his word in such a way that God is glorified:
Do your best to present yourself to God as one approved, a worker who has no need to be ashamed, rightly handling the word of truth. [2 Timothy 2:15]
But as for you continue in what you have learned and firmly believed, knowing from whom you learned it and how from childhood you have been acquainted with the sacred writings, which are able to make you wise unto salvation through faith in Christ Jesus. All scripture is breathed out by God and is profitable for teaching, reproof, correction, and for training in righteousness, that the man of God may be complete, equipped for every good work. [2 Timothy 3:14-17]
I often go to 1 John 2:28-3:3. God never fails to remind and to encourage me there to trust him in what he says he has given me in Christ and who he says I already am as I live out my faith in this life. And even more in what I will have and be in Christ forever when he returns. Praying you may read it and find there the same. Whether this passage is for you new or well-trodden ground, it is good and solid ground.