I should note that when building the first copy of a new design, I meter out the bare board before populating it to catch the shorts that accidentally got designed in the layout.
If the metering out process seems to be okay, I attach the power connector, apply power and assuming the power supply doesn't fault out ("crowbar" in railroad electric traction parlance—not the technically correct usage), I check all points that are supposed to be powered for the presence of power.
With the above checks handled, I populate the board, periodically checking for a low resistance or short between Vcc and ground, especially after installing an electrolytic (POC V1.0 had a reversed electrolytic error that I caught during assembly-stage testing). By the time the board is fully populated I'm reasonably confident that I'm not going to power up into a catastrophic fault. That, of course, doesn't mean that a defective part couldn't go bang, but in practice, that has very seldom happened. In fact, it's literally been years since I last got a new IC that was defective.
The above process may sound like something a Nervous Nellie would do, but in practice it has saved the day more than once. Burned-up carbon comp resistors don't smell very good and I especially loathe having to clean up after an improperly-installed electrolytic blows following power application—had that happen in a 100 watt vacuum tube PA amp and, boy, did it make a mess of things.
Something that could be done when first-time powering a gadget is to insert a low wattage incandescent lamp in series with Vcc to act as a fault current limiter. I'm "braver" than that and depend on the power supply to automatically shut down if a fault occurs. That may not save parts but it will in most cases prevent PCB damage so a
post mortem can be conducted.