I wouldn't say impossible.
Well, God and His ways are beyond me; I cannot see into His secret council. I am not 100% convinced of a young earth, nor am I 100% convinced of an old earth. Though I do lean towards an old earth.
I find it interesting how young earthers can say the first six days were a literal 24-hour period, and I heard it said by some, we are not through the seventh day yet, so the only day that isn't a 24-hour period is the 7th day? There is a problem with the 7th day, I suppose. If God made everything in six days (periods of time), then the seventh day, if it we are still in it, fits right in as a period of time. Old Earth would make sense.
Is there an 8th day?
Personally, I do not believe we can read Genesis and come to a positive conclusion that the six days were literally 24-hour periods. An old earth does no damage to Genesis whatsoever.
Does it make a difference? Some reformers like John Owen, whom I admire greatly, say it does matter, and he believes in a young earth.
I just do not see how.