To some Old Earthers, accepting an Old Earth is necessary because God simply wouldn't be strong enough to create everything in just 6 days. But far more common are those who, though they acknowledge He is powerful enough, claim that Biblical Creationists are the ones limiting God's ability. Who are we to say God would not be capable of using the Big Bang, or Evolution, over millions of years, in order to create?
There are two ways to approach the question "could God have created this way?" The first is to ask whether or not it is within His ability. The second is to simply ask what the chances are that He did. If God is able, that still doesn't address the likelihood that He did. God is able to give every man on Earth our own pet unicorn, He has not done this.
The answer to the latter question is very obvious: No, God absolutely could not have used Evolution or long ages. Although the Bible does not go into perfect detail, it does give us enough details to know that Evolution and millions of years do not fit the Bible. Attempts to make them fit are, to put it nicely, extremely weak, and seemingly disingenuous. For the first 1,700 years of Christianity, no one even tried. "Young" Earth Creationism (as if 6-10,000 years could be considered young) has been the dominant interpretation from the very beginning of our faith, whereas no one started trying to compromise with long ages until the atheists started saying long ages are scientifically confirmed. It is weakness of faith, not any kind of reason, that compels a Christian to accept long age dogmas.
The answer to the former is not so clear cut. Does God have the physical ability to create over long ages using Evolutionary processes? I contend that the answer is still no. See, the concept of omnipotence is often misunderstood. There are plenty of things the Bible explicitly tells us God cannot do, such as lying (Hebrews 6:18; Titus 1:2). So, there are things God cannot do. How do we determine what those things are?
2 Timothy 2:13 gives us the answer to this by telling us another thing God cannot do. He cannot "deny Himself". In other words, God is internally consistent. God cannot create a round triangle, as is often asked, because that is incoherent. Omnipotence, rather than being understood as being able to do literally anything including the incoherent, is better understood as this: The only limit on God is God.
Now, we know that God is more than capable of doing just about anything that is logically coherent in His creation. If He wants to use a magical explosion to create, I have no doubt He would do that. However, the instant you add death before sin, you add injustice. Is it possible for God to be unjust? Re-read 2 Timothy 2:13. This doesn't just tell us that God cannot deny Himself, but that, as a result of this, He is faithful even when we are faithless (a fact OECs and the like can be very grateful for). Would God cause blind pitiless indifference even before sin entered the world? By no means! The horrors that would be required for Evolution to occur were simply not possible before there was a man to sin, so how could they have brought about that sinning man?
With all of this in mind, I do not feel any hint of reservation when I say that no, God absolutely could not have used Evolution to create. Not only does His infallible word quite clearly tell us that this is not what happened, it also presents a God who is internally consistent, and certainly not psychotic enough to cause such a brutal process, much less call it "very good". No, God could not use Evolution.