Any boat much larger than a canoe has to be pumped periodically to stay afloat.
In modern ships the biggest source of seepage is via the drive shaft. Water steadily trickles and sometimes even pours in and must be pumped out.
Wooden ships seep all over. Merchant ships in the 19th century had brass bilge pumps that took four men to operate. It was hard work.
The alleged size of Noah's Ark puts us way beyond a clipper ship, not just in terms of the amount of bilge water, but in terms of how high it would have had to be lifted.
We're talking pistons, crankshafts, rings, valves, reinforced hoses and an external power source that can spin at several horse power.
--Way beyond the scope of the story.