New Toto Drake-Hissing sound

We are having a problem with a brand new Toto Drake toilet.

Approximately 40 minutes after flushing, the toilet begins to make a hissing sound which sounds like water running. It stops when I turn off the water supply to the toilet. I looked in the tank, and it sounds like it is coming from the blue G-Max valve-it has caused a leak in the room below--
does this mean the G-Max valve is faulty?

yes, toss in a fluid master 400-a or replacement fill valve of your liking

Don't replace a part this is working.

It may be that the flapper is leaking.
The fact that your fill valve doesn't start to refill for 40 minutes is a good sign it's the flapper and or a leaking tank.
No sense touching the fill valve if it's just refilling the tank.
Turn the water off to the tank, and see if the water level drops. If it does, you have a leak somewhere in the tank.
Check the bolts and make sure they aren't leaking.
You can put food dye in the tank and see if the flapper is leaking.

If there is damage below, it would more likely be the seal at the floor that is bad.
Did the wax compress when you set the bowl?

If the tank is leaking to the next floor, have you checked to see if the bolts holding the tank to the bowl are tight?
Below are instructions for installation.

https://terrylove.com/forums/showthread.php?743-Installing-a-Toto-Drake-CST744S-2-piece-toilet

Update:

With water turned off, water in the tank did drop, and food dye did go into the bowl. So this implies it is a leaky flapper, correct? (Isn't that unusual in a brand new toilet?). There is no water on the floor around the toilet bowl.

Since water is leaking to the level below, does that also imply that there must be an improper seal (either wax gasket issue or bolt issue) between the bowl and the floor? Otherwise, wouldn't the water leak from the tank just go to the bowl and out to the drain?

The two are independent. Call Toto, they'll send you a new flapper. They don't make them. Every once in awhile, it happens. You may also notice in a day or so, that it stops...the pressure from the water may reform the thing. Also, check the surface of the flush valve (where the flapper fits) - it could have a little plastic nub or something on it. Also, (this is a two-piece?), the nut on the bottom of the tank that holds the flapper seat in place might be a little loose. It's always a good idea to double check that is tight before installing. Usually is, but it might not be.