I always bake brownies over a "sling" of parchment, which is a strip of oven-safe parchment paper that is draped across both sides of the pan so I can lift the brownies out onto a platter or cutting board after it is done baking and has cooled a bit. It keeps the brownies from sticking to the bottom of the pan and allows you to place the entire slab of finished brownies onto a flat surface for cutting without having to "scoop" the brownies out of the pan to get out that first piece.
But let's say you either neglected to use parchment paper or don't care to use that technique.
The reason that second pieces comes out so cleanly is because you created a bit of room to lift out that second slice after you removed the first. So… one way to get a better "first slice" is to actually cut two slices before you try to lift out that first piece. The extra cuts gives you just a bit more space to lift out that first slice cleanly. By cutting two slices, you create a bit more room to lift out the first without having it crumble into pieces as you try to lift it out.
This also works well for pies. Cut two slices initially to create a bit of space between the slices so the first slice will lift out cleanly.
Try it. It works.