Can filling up a 75 gallon water heater tank without opening a faucet cause damage?
I wouldn't worry about it at all. A gallon of water is roughly 213 cubic inches.  Assuming that you filled the tank completely (which is unlikely - see below), you would have displaced 213 * 75, or 15,975 cubic inches of air inside your plumbing. One atmosphere of pressure (14.7 psi) is defined as the pressure exerted by a 33.8 ft column of water. Assuming that all of the pipe in question is 3/4", you would have increased the pressure by 14.7 psi if the total pipe length was 472 feet.

But what actually happened is that the tank stopped filling when the air pressure reached equilibrium with the water pressure.  The water that you filled the tank with was coming in at whatever pressure that your household water supply has (typically this is somewhere around 40psi).  When the total pressure in the plumbing system reaches 40psi, the tank simply stops filling because there isn't a pressure differential. So basically, once the air you were displacing reached the pressure of your water supply, it would have simply stopped compressing it because the tank wouldn't be filling any more.