The increase of pressure occurred billions of years ago when the Earth was originally formed from the cloud of gas and dust accumulated in a disc around the early Sun.

The collisions between particles created a lump that started attracting more and more particles and dust and larger debris pieces. As the mass increased, gravity also increased and each layer started to push on the layer under it with increasing weight. Eventually the force of gravity was strong enough to slowly deform the core of the object, until the proto-Earth reached a state called hydrostatic equilibrium.

In English this means the object was now big enough that it formed into a sphere under its own weight. This shape change caused a lot of heat through friction, and of course the Earth was not yet done growing.

As the planet grew and the pressure within increased, the core started to melt, which meant that heavy elements sunk into the core. However, eventually the planet grew so big that the pressure at the core actually started to solidify the iron and nickel there.

This is how Earth ended up with a solid iron-nickel inner core, surrounded by a thick layer of outer core which is also mostly iron and nickel, but in liquid phase.

So, the pressure increase that caused the Earth's core to heat up originally occurred billions of years ago when the planet was forming.

Currently, it's believed that some of Earth's core heat is still residual or "primordial" heat from the formation of the planet, and the rest is from tidal forces generated by the Moon, or heat from radioactive decay of active isotopes.