Suspend the brake paddle once braking is initiated.

[Squirrrel]

Today morning, while driving my 2016 Suzuki GV, I pressed down on the brakes hard. From then on, whenever I pressed down on the brakes, they would apply, but I could tell they weren't fully applied because the paddle would sink deeper and the car would slide ahead. The braking fluid pressure builds up when I apply the brakes a second time, right after the first. However, even after applying the brakes a second time, the paddle sinks in even further. I got where I was going by repeatedly slamming on the brakes. Under the vehicle, I made sure there was no leaking braking fluid. Possible explanations?

[Grundysp]

Have you made sure that there is no brake fluid leaking at the point where the brake pipes attach to each tire? Wetness or discoloration will be visible there if a leak is present. Leaks in the brake vacuum hose or the brake fluid are the most common causes of a sagging brake pedal.

[Grundysp]

Amazon.co.uk : brake fluid

[Mezuzzi]

The brake fluid on my Swift Sport was old and had an excessive amount of water, which caused it to have a low boiling point. and because the fluid condenses into gas when it boils, the pedal collapsed to the floor as I pressed down on the brakes.

although it might be the ABS's fault. I've heard that your ABS unit will die fast if the fluid is too watery.

[Preedom]

So, if I'm reading your post correctly, you can apply more pressure by pumping the brake pedal?

I was wondering when you last changed the brake fluid.

The fact that you should change your brake fluid every couple of years is mainly due to the fact that it is hygroscopic, meaning it absorbs water. This is explained above.
Because of the water content in old brake fluid, the boiling point of your brake fluid is much lower. This means that when you come to a sudden stop, the heat from your brake pad and disk will boil the fluid, transforming it into gas. Gasses are obviously useless as hydraulic fluids; when they compress, they let your brake pedal go all the way to the floor. In such a case, you can rapidly restore hydraulic pressure by pumping the pedal.

[Grundysp]

sure enough. It slipped my mind. So far, I've had success with pedaling.