Elon Musk has stated that he will consider it a success if the Falcon Heavy gets far enough away from the launch pad to not cause damage if it blows up. The Falcon Heavy underwent a 12 second static fire. Let's say there was some critical issue that wouldn't show up until just after the duration of that firing. Would the Falcon Heavy be far enough to not cause significant damage to the launch pad in 12 seconds?
Not even close. In fact, at 12 seconds in, you're looking at maximum damage to not just the pad itself, but the surrounding area as well. You're going to have tons of debris (most of it burning and possibly carrying even more unburnt fuel) fall from 1500-2000ft range in a giant umbrella of destruction.
In 1997, a Delta II carrying the GPS IIR-1 satellite exploded 13 seconds in. While nobody was killed, check out the video of what happened to the vehicles parked outside the blockhouse.
According to the Falcon Heavy press kit, the engines are lit about 5 seconds before launch. The acceleration should be a bit faster then a standard Falcon 9 mission. Let's look at the last launch seen below:
In the above image, at T+0:09, the rocket still appears to not have cleared the tower. I'm sure the Falcon heavy will accelerate quicker, but even at T+0:12, it still is only a few hundred meters above the ground. It takes until T+0:25 until it is a full kilometer away.
A few other points of reference. Max Q happens at about 1:06 for Falcon Heavy, 1:10 for Falcon 9. It seems that the acceleration won't be significantly higher during the early stage of flight. The biggest gain seems to come from using the middle core less until outside of the atmosphere.
Bottom line, if anything that results in an explosion within the first 30 seconds after engine ignition happens (T+25), I strongly suspect there will be significant damage to the launch pad. And if it happens within T+15s of launch there will almost certainly be at least as major of an effort to fix as with the previous explosion.
To avoid damage to the pad, the rocket must have traveled down range far enough that if it exploded, the debris would not land back on the pad. The issue isn't height, it's horizontal distance. 12 seconds, as mentioned above, wouldn't get you downrange much. 30 seconds definitely would.