There are a lot of good points throughout this thread, and a lot of ideas on how creation may have happened.
I spent a lot of time investigating it and I found - simply that none of the ideas or models completely satisfied me from a scientific standpoint. They each contain good ideas, but there is also one or more irreconcilable problems in each of them for me. So I'm not coming down in support of any position. I'm much better able to point out the problems in them. But that won't help you.
I see your main question is how to reconcile old earth with Creation. There are several schools of thought that I'm aware of.
One involves some quantum theories that I'm not qualified to comment on. I reached this near the end of my investigation, and it has been updated. Much of my science background is in biology, not physics, so I'm not really equipped to evaluate it, but it did have some very interesting ideas.
Another involves the possibility that the "days" in Genesis are not literal days. Scripturally this can be supported as the word translated "day" is yowm or yom, which can be translated as "daylight hours" "day" or even "long period of time". In order to adhere to this one, one has to accept that some other source of light supported the plants (created on the third day) and the sun (created on the 4th day). However, God said in the very beginning "Let there be light" so we do know there IS another source of light. While it might not fit our understanding, our understanding is obviously limited, since we have no knowledge of such a powerful light source other than the sun/stars. However, in Revelation, it is stated that the New Jerusalem will have no need of the sun, since God Himself will be its light, so that is the most likely explanation I can see. (However, you still have to deal with "evening and morning were the first day" and so on, and that is harder to explain away.)
Some simply see Genesis as a metaphorical story. This easily makes everything fit, since you don't have to be literal. And it is not impossible that it would be so. The problem is that if you see Genesis as metaphorical, what else can you choose to be metaphorical, and how far will you take it? At some point it does create a problem for the faith, if for example you begin to believe that Christ Himself was a metaphor. (That doesn't make Genesis as a metaphor not true, it's just the concerns I've seen addressed by others over that position.) And personally, if Genesis IS a metaphor, I don't have a problem with that, but I still believe God Himself is responsible for creation, by whatever means.
One other position that comes to mind involves a creation prior to the one we know. This idea is generally presented with Gen. 1:2 and Gen. 1:28
Gen 1:2 The earth was formless and void, and darkness was over the surface of the deep, and the Spirit of God was moving over the surface of the waters.
This can also reasonably be translated as "the earth became desolate, a ruin where nothing was left, and death/destruction was on the surface of the abyss/waters, and the Spirit of God brooded/moved above the surface of the waters"
This is often connected with God's instructions to the first man and woman after creating them.
Gen 1:28 God blessed them; and God said to them, "Be fruitful and multiply, and fill the earth, and subdue it; and rule over the fish of the sea and over the birds of the sky and over every living thing that moves on the earth."
It has been noted that what is translated here as "fill the earth" is the word male' which can be translated "replenish", so that the first couple are told to "Be fruitful and multiply, and replenish the earth."
These two verses are taken together to imply that while the earth had already been created, SOMETHING happened to destroy it, and it now needed to be re-filled, and God's intention was to do this with animals and people.
This does rather conveniently sidestep many of the issues that cause a problem with other models. It allows for old earth, and yet still Creation. I admit there is an appeal in this model for me as well, though I don't promote anything as truth (other than Scripture), only possibilities.
But a further reason this appeals to me is that in Job 38:4-7 we have an indication that angels were present when God formed the earth. Yet in the creation account, there is no mention of having created the angels. So it falls before the creation account, and yet is not explained anywhere in Scripture. Obviously Genesis does not include some things about creation and what does not pertain to us, so we can't know what may or may not have happened. (I used to think the angels were created along with the sun and moon, but in Job it says they sang and rejoiced when God laid the foundations of the earth, so ... I believe there is more evidence that they were created before the earth.)
I will say though, that after spending a LOT of time trying to sort this all out, it became less important to me. I realized we don't have to know, we just have to believe God.
In your case, if it gets in the way of believing God, then I understand the need to find a way to mentally reconcile things. If we simply push something to the back of our minds and pretend it's not there, it can erode our faith and on some level we know that we've been intellectually dishonest with ourselves. It is my firm belief that God can stand up to close scrutiny on our part, even if we can't find the answers, so I don't think it's wrong to encourage people to investigate anything they feel a need to investigate.
However ... I doubt you (no offense, or anyone else) can reach full 100% certainty and find all the answers, given what we know right now. But certainly investigate to the point that your doubts dictate.
