As far as goalies who started their careers with a long "shutoutless" streak before eventually getting some, Jeff Hackett didn't get one until his 164th regular season appearance.
That may or may not be the longest stretch from the start of a career. Ed Staniowski's first shutout was somewhere in the 138-182 game range. John Garrett's was in the 152-168 range. So they may have Hackett beat depending on when they got their shutouts.