Growing the beard refers to the maturation of TNG. That the series grew into its own around the time Riker grew his beard out. When do you think DS9 grew its beard and came into its own as a series?
As a show, season 2, but not all the characters caught up. IMO- Sisko grew his s2 or 3. Bashir grew his in s3 or 4. Quark and O'Brien had their beards already in S1. Odo learned to shape shift his beard in S2. Kira grew her beard in S2 Dax grew a goat in s2 or 3, then finally grew a beard in 5 maybe.
Season 4 episode 1, it began to grow it's own legs. I know the Klingon thing was a year setback for the writers and all but adding Worf, rebooting the credits and creating the tension of things to come really took off. Seasons 1-3 were great so I don't want to dismiss them...Season 4 is where we got to have DS9 inserted into the rest of the alpha quadrant as opposed to the alpha quadrant coming to them. I mean they were always heading through the wormhole, until season 4 the alpha quadrant was kinda more foreign to the show then the gamma quadrant. I like that the show went from exploring the gamma to defending against what was there... I liked all the characters from the beginning except Dax. She got more palatable to me when she was able to play off of Worf. I have a thing for crazy women so Kira never bothered me...
I'd say the beginning of S4 marked the beard coming into its full form, but it started growing as early as "Rules of Acquisition", with the first mention of the Dominion, and certainly by the end of "The Jem'hadar" it could no longer be mistaken for a bit of dirt on the face. S3 marked a slow but steady growth of the beard.
I think it was a very gradual process for the series to finally come into its own but the series did improve almost immediately. The 1st several episodes featured terrible acting and hamfisted plots. After about 8 episodes, minor characters started to get mixed in and the plots became more interesting and the actors started to step up their games.
Season seven is variable. It doesn't feel like its jogging on the spot as much as TNG's seventh season did, but the growing crescendo that had been building through seasons three through to the end of the sixth season felt like it got deflated a bit in the early parts of season seven. "Take Me Out To The Holosuite" has got mixed reactions, to be sure, but to me it does feel somewhat like filler when we've had three seasons of solid meat preceding it. Also, the need to establish a new regular character meant that a number of episodes felt like 'Stop Here And Do An Ezri Scene'. Arguably, the show probably didn't hit its stride again until at least halfway through the season, when it overcame these hurdles and got back on track. YMMV, of course.