Seems like the wiki article you linked covers it fairly well:
Bombing of Normandy began around midnight with more than 2,200
British, Canadian, and American bombers attacking targets along the
coast and further inland
Minesweepers began clearing channels for the invasion fleet shortly
after midnight and finished just after dawn without encountering the
(all emphasis mine) It wasn't exactly a stealth mission. The bombardment began and provided cover fire to enable the minesweepers to approach.
An interesting discussion of the process from one of the individuals involved can be found here:
Our ship, which was on the port side dropping buoys, had the job of
giving a sharp blast on the siren each time a buoy was dropped, so
that the buoy layer on the right hand side would drop its buoy at the
same moment. The awful noise of the siren made us wonder if the
Germans wouldn’t hear us coming, but nothing happened. Our own light
coastal forces were out in strength cruising around, waiting to give
us cover if we were attacked.
So, not a quiet process, or secret by any means.
The minesweeping process of the time involved cutting loose the mines and then detonating them on the surface with gunfire.But again the bombing taking place might cover any detonations. (Image from wikipedia)
So between detonating mines, siren blasts, and overhead bombers attacking the coast, I don't think they were expecting secrecy at this point.