How did God bless the world through Abraham? Genesis 12 says he would bless all nations, but most nations don't follow the Bible.
Blessing is a major theme of the Bible. In the book of Genesis, people who come into contact with Abraham and his ancestors often prosper. I will leave it to you to trace this theme in Genesis. But of course the broader promise is international. The Lord intended to bless the entire world through Abraham's seed--and so he has. Abraham fathered Isaac, who fathered Jacob... Judah.... David.... Jesus Christ. (See also Matthew 1.) Through Christ, millions have come to a saving faith all over the planet.
Yet because the Lord brings the word through other people, when his people are silent and do not speak up, the gospel does not spread (Romans 10:13-17). May we who are Christians pray for God to use us as his vessels (2 Timothy 2:20-21), so that the gospel may bear fruit in all the world (Romans 1:8; Colossians 1:6,23). And at the end, we can expect a huge multitude from every nation to have been reached with the gospel (Revelation 7:9).
In addition to Genesis 12:3, you might take a look at Genesis 18:18, 21:12, 26:4, 28:14, 49:10; Exodus 19:6; Deuteronomy 32:43; Joshua 2:10; 1 Kings 8:43,60; 2 Kings 19:19; 1 Samuel 11:1ff; 2 Samuel 7:13-14; Psalms 22:22,27, 89:4,36, 96:3, 105:1, 132:12; Isaiah 2:3, 49:6, 55:5; Jeremiah 12:16, 23:5, 33:15; Micah 4:2, 7:11; Haggai 2:7; Zechariah 2:11, 8:23; John 10:16; Galatians 3:8,29.