Nope, it's not impossible. Here's why. The ark was big enough to hold 530 railroad cars. They put 250 sheep in a railroad car these days, so that's 132500 sheep size animals. Yea, I know there's a lot more types of animals than that, but God only needed to preserve one of each kind of animal. He didn't need every species of dog, or cow, or giraffe, or cat. He only needed two of each kind and let the gene's that He designed do the rest of the work when they left the ark. Gen 8:19 Every beast, every creeping thing, and every fowl, and whatsoever creepeth upon the earth, after their kinds , went forth out of the ark. I mean, God is God. Why would we limit what He can do when He's the one who spoke them into existence in the first place? It only sounds impossible if we think about trying to do it without God. Then I think it would be impossible.
Some say it was just a local flood only in the middle east, but that is not what the bible says. The whole earth was flooded just as the bible says, and the evidence is everywhere.
Gen 7:19 And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered. 20 Fifteen cubits upward did the waters prevail; and the mountains were covered.
You can't cover the mountains with water and have the valleys dry...
Also, if it was just a local flood, why didn't Noah just move away? He had over 100 years to build the ark. He could have just moved his family in that amount of time.
People also ask: How did they take enough food for everything? Remember the two times in Matthew 14 and 15 where Jesus fed thousands of people with a few fish and loaves of bread? God can do anything and He simply took care of it. No mystery or impossibility. If God weren't involved, yes, it would have been impossible, but God is not limited like we are, He is God.