What is the difference between seeking the kingdom (Matt. 6.33) , and seeking God (Psalm 34.10) and how do we know when we have achieved these things to God’s satisfaction? In other words we have fulfilled the conditions so that God can begin to bless.
Where the result is concerned, the two verses are essentially the same. Psalm 34:10 is in Old Testament language and required obedience to the Old Covenant. Matt. 6:33 is in New Testament language and requires being born again and submissive to the Lord’s will for our life. I don’t think these verses are about blessings, as we think of them. I think they are about God helping us to make sure our needs are met.
If you’re a believer, you’re already being blessed because God is working everything together for your good (Romans 8:28). Therefore, it sounds to me like you’re looking for increased material blessings.
For verses on material blessing, I suggest you look to Luke 6:38 and 2 Cor. 9:6-11. But don’t make the mistake of doing these things solely with the expectation of being blessed, because it doesn’t work that way. God blesses us when we show our gratitude for what we’ve already been given by giving to others without regard for any future reward.