At bottom, there is no scientific argument against the declaration that God created all that there is last Thursday.
Personally, I see perfect harmony between Genesis and science because:
b) The perspective of time (space/time) passing changes from the inception of all that there is in Genesis 1-3 to earth in Genesis 4 when Adam is banished to mortality.
c) Relativity and inflationary theory tell us that time is relative. Six days from the space/time coordinates of the inception of this universe is equal to roughly 14 billion years from our space/time coordinates on earth.
Schroeder: Age of the Universe
In case you want to know, this exponential rate of expansion has a specific number averaged at 10 to the 12th power. That is in fact the temperature of quark confinement, when matter freezes out of the energy: 10.9 times 10 to the 12th power Kelvin degrees divided by (or the ratio to) the temperature of the universe today, 2.73 degrees. That's the initial ratio which changes exponentially as the universe expands.
The theological difference hinges on the interpretation of Scriptures, particularly Romans 5:12-14 and I Corinthians 15:42-48. A large segment of Christians (including Roman Catholics) view Adam as the first ensouled man, a smaller segment view Adam as the first mortal man.
My musings are squarely in the middle, i.e. 6000 years since Adam at earths space/time coordinates plus 6 days from the inception space/time coordinates and Adam as the first mortal man with the breath of God (neshama Genesis 2). All other creatures in Genesis 1 have a soul, a nephesh, but not a neshama.
It is a waste of time to argue a theological point such as YEC using science. It is doctrine and must be argued with Scripture, lexicons and ancient manuscripts. If one is unable to make such a theological argument, I suggest it is better just to ignore the YEC post altogether.
Among Christians are those of us whose vision of the Word of God is Jesus Christ Himself (John 1 and Rev 19) that the Word of God is alive and speaks to us by the indwelling Spirit (I Cor 2, Romans 8, John 15-17) to lead us into Truth. To us, the Scriptures are inerrant but do not substitute for His Person.
There are other Christians who put Scriptures on par with Tradition of the Church. The interpretation is made by the Church leader, or Pope, who is to be received as the vicar of Christ on earth.
And there are other Christians who put the emphasis on the Scriptures themselves. These will more often refer to the Scriptures as the Word of God.
And then there are the Christians who are cavalier about all of this.
Thus, when you ask:
When a believer perceives a conflict between Genesis and science since God is author of both the believer must conclude that either (a) he doesnt understand either the Scriptures or the science or (b) that he must accept the Scripture on faith.
I think you have a supurfluous alternative there, specifically your (b). I believe that your alternative (a) says it all. There's an error in his understanding of science or scripture which results in an apparent conflict.
However, as you said later on, if the believer is unable to resolve the meaning of scripture and science, then he will rely on scripture -- if that is the imperative of his theology. That, alas, may put the believer who knows no science, and who may mis-interpret scripture, in the position of (pardon the expression) a "flat earther."