Please read to end: I believe that the answer you are looking for is in Gen 2:4 These are the generations of the heavens and of the earth when they were created... Genesis 1 lays out the whole order of creation in general, but Genesis 2 focuses on the "generations", the bloodline, because that is the focus for Man's redemption eventually through Jesus' blood. I agree that there were other men and women created on the 6th day, but Adam and Eve were the first. Also, Adam was created 'BEFORE' the plants and herbs were in the earth.
Gen 2:5 And every plant of the field before it was in the earth, and every herb of the field before it grew: for the LORD God had not caused it to rain upon the earth, and there was not a man to till the ground...
Gen 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
Now Adam was formed, but the earth was not completely ready to sustain him, so...
Gen 2:8 And the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed.
Here is the answer to some of your controversy, there were other people on the earth after Adam, who were created on the 6th day, but ONLY Adam and Eve were specifically given a garden by God and were in the garden of Eden. Thus, when they left the garden to till the land, it was then ready to produce. Also, there would've been other people for Cain and Seth to marry.
Additionally, Adam's bloodline is ours because Noah and his sons were descendants of Seth of Adam; here again, we see the importance of Adam's generations as the focus of God's story for the redemption of Mankind.