So, then where did this master engineer make room for all the animals?
The Bible says that God brought the specimens to Noah, so they were God's choice not Noah's. It also said that each "kind" was brought into the ark, not every "species" of every kind. And it was only land dwellers.
Noah spent the best part of 5 decades building this vessel and in his instructions were the all the necessary foods required to feed all of the animals and the humans. Most were probably vegetarians because some of the largest and strongest land animals are herbivores. Humans did not eat meat before the flood so perhaps animals didn't either.
In prophesies pertaining to the future it is said that
"the lion will eat straw just like the bull"....so perhaps we will all return to being vegetarians. The only meat eaters would have been carrion creatures designed to clean up any creature that died. They don't kill their victims, but make sure that nothing is left to pollute the earth.
The ark was enormous—some 437 feet (133 m) long, 73 feet (22 m) wide, and 44 feet (13 m) tall. It was far larger than the largest seagoing wooden ships built even in later centuries. It was three stories high with compartments that would have housed the animals, and with plenty of room for storage and living space. It is not out of the realms of possibility that God could accomplish this. He created them all in the first place.....and besides, it serves God well as a pictorial example of what was to come in the future. (Matthew 24:37-39) God did not save Noah....but told him how to save himself.....he does that with us too.