. . . and without strict philosophical precision. (If you want the fuller, more technical and philosophical explanation, go here.)
Every moment in time logically and necessarily implies a preceding moment. Therefore, when God created the universe (and in the concept of "creation" here is included not just the original six days but also all of the foundational events that shaped the cosmos into the form in which we know it today--that is, all the events in Genesis 1-11), he created it with a back story. So the world he created was not created in a new condition, but with a previous history extending back infinitely. This is true of the world as a whole and also of the individual parts of the world. Birds, for example, when they were created, were created with a previous history which may have included events such as their being descended from dinosaurs.
Both the creation history of Genesis 1-11 and the previous history created by those creation events are quite real. Neither of them is illusory. So it is not that God created birds with the appearance of having a previous history they did not in fact have. Rather, it is that God created birds with an actual previous history. The difference between the Genesis creation history and the created previous history is not that one is real and the other is not, but rather that the latter is a product of the former and is appended onto it as a back story rather than the main story. Think of a novel, in which there are events that take place within the novel itself and also other events that are part of the assumed history of the novel but which never actually happen in the novel--the back story.
Therefore, we can say that the world was created a few thousand years ago in the space of six days, and that all the other events of Genesis 1-11 actually occurred in history, and at the same time not be in disagreement with the claims of the modern mainstream scientific community that the universe is 14 billion years old, that life developed over billions of years on earth, etc. (The Neo-Omphalos theory doesn't say positively that the mainstream scientific community is right about these things, but it shows that their view of history does not contradict what the six-day reading of Genesis says in these areas.)