in which rejoice, if presently proper for little time made sorrowful in various trials so that the proving of your faith (more precious than gold that perishes) proven by fire, now found to the extent praise and glory and honor in revelation Jesus Christ (1 Peter 1:6-7)
There is a time and season for all things, a time to weep, and time to be sorrowful just as there are times to be happy and joyful, the wise King Solomon said. It proper for a time that various trials take place so it proves you and tests you. The word proving δοκιμάζω (dokimazō) speaks of trials that prove you, to approve by testing. There is a lot to the meaning of the word proving. The purpose of the proving is so that you are found to the extent praise and glory and honor in revelation Jesus Christ.
and just as not proving to have God, God gave them over to an unapproved mind to do that not fitting (Romans 1:28)
Even though God was revealed to them and they knew God they did not have approved minds so they did not give God glory and honor and praise. In their minds they proved to not have God. Now, as new spiritual creations in Christ we have the power within to obey God's spiritual laws but our minds need to be renewed so that we can approve of the things of God that which are good, pleasing, and acceptable (Romans 12:1-2). To have an approved mind then is to approve of God's will as good, pleasing, and acceptable. Trials are the proving of our faith, and the root word of faith means to be persuaded. Therefore one way God renews our minds is by proving our faith in various trials.
making mention of you in my prayers so that the God of our Lord Jesus Christ, the Father of glory, gives you a spirit of wisdom and revelation in knowing him (Ephesians 1;17)
The goal of the proving is to be found to the extent praise and glory and honor in revelation Jesus Christ. Nothing is more precious to God, we can give all the gold we want, but if we lack having an approved mind, we are not to the praise and glory and honor of God in revelation of knowing Jesus. Jesus is from God our wisdom (1 Corinthians 1:30-31). May we have a spirit of wisdom and revelation in knowing Jesus more and be approved of God.