During TNG, the accepted formula is that 1,000 stardate units equates to 1 calendar year. There's a nifty calculator on DITL that lets you use that formula to work out the exact date of any given Stardate.
In Encounter at Farpoint we see that the Stardate is 41153.7, with equates to Wednesday 26th February, 2364.
In All Good Things we see Picard arrive at the ship for the first time. We're told the Stardate is 41148, which is Monday 24th February 2364 - just two days before he made his first log entry in Encounter at Farpoint.
In the episode Data's Day, the Stardate is 44390.1, which means it is set on Tuesday 23rd May, 2367. Interestingly, Data comments that this is the 1,550th day of the Enterprise-D's service life. If you subtract 1,550 days from 23rd May 2367, you find that the Enterprise-D entered service on Saturday 23rd February, 2363.
So the ship was actually in service for one year and one day before Picard took command!
Now "in service" can mean different things. One can presume that the E-D spent that time working up, training the crew, working the kinks out of the systems, etc. But even for that, surely there would be a commanding officer on board the ship, yes? And it's even conceivable that the ship undertook actual missions during this time.
So was there a commanding officer for the Enterprise-D before Picard? It seems that there must have been! One wonders who it was...