The dimensions given to the ark are 300 cubits long, 50 cubits wide, and 30 cubits high. The cubit probably refers to the Royal Egyptian Cubit, the most standard unit of measurement at the time. This means the ark was 500 feet long, 85 feet wide, and 50 feet high.
Now consider that it had to be assembled using NO metal nails or fasteners. Such technology was not available at the time as nails were not around until the early Roman Empire. One of the largest wooden ships ever built was the Pretoria, a barge used on the Great Lakes. It measured 338 ft long, 44 ft wide, and 23 ft in depth. That's roughly half the size of Noah's ark and the Pretoria was barely seaworthy. Even with iron bracers and clamps, the ship still required a pump to constantly pump out water that leaked into the ship. There is no way Noah could have built a ship to the size of the ark and had be even remotely sea-worthy, it would have sunk like a brick. There is a size limit when dealing with wooden vessels and the ark exceedes that by several orders of magnitude.
Additionally, there was no realistic way for Noah to build the ark. He couldn't have used a drydock configuration, that technology wasn't available. There were no cranes available to lift him the 50 feet off the ground and he apparently didn't have much help holding the timber in place. On top of all that, the man was a wine-maker, not a shipbuilder. You cant just wake up one day and say "I think I'll build a ship!" and have it work first time. Shipwrights are EXTREMELY experienced people who spend decades learning what they do.