Don't put the meat on with thick white smoke. Over time as it burns down you will see the thick smoke start to thin, and eventually be a very thin and faint blue. Not long after that you may not see any visible smoke really at all. Don't worry, your meat is still getting smoke flavor.
On a WSM using minion like you are, it isn't uncommon for the smoke to take upwards of an hour to settle down before it's ready.