The question of water delivery to Earth, and planets in general, is one that is hotly debated!
Let's start by using Earth as our benchmark. The total amount of water on the Earth's surface is around ~1.5 x 1021 kg, and we refer to this amount as one 'ocean' of water. There's also a huge amount of water inside the Earth itself, locked in e.g. hydrated silicates and in the core. We don't know how much this is, but estimates range from about 1-50 'oceans' worth. So any models that attempt to describe water delivery already have a problem because we don't fully understand how much water there actually is!
One important feature of Earth's water is that it has a distinct D/H ratio (the ratio of deuterium to hydrogen), which is ~6 times higher than that of the Sun and the gas planets in the Solar System. We can use this fact to constrain where exactly in the Solar System Earth's water might have come from. Current theories suggest that carbonaceous chondrites are a likely source.
So let's take a look at some of possible delivery methods during Earth's formation within the protoplanetary disk:
Direct accretion of water from the protoplanetary disk
Water may have been accreted directly from the disk in the form of water vapour adsorbed on to silicate grains. This scenario could have seeded the Earth with a few 'oceans' of water, but doesn't account for the high D/H ratio.
Alternatively, a planet may accrete water in the form of solid pebble 'snow' if the planet exists sufficiently far away from the star beyond the water snowline. This is not the case for Earth, but is certainly an important mechanism for planets in general. It is important to consider the fact that protoplanetary disks are dynamic systems in which the snowline isn't static. Depending on the conditions, a static planet could see the snowline sweep past it during the course of its formation.
Reactions with Earth's early magma ocean
Gravitational accretion of hydrogen from the protoplanetary disk may have reacted with the early Earth's magma surface to generate water. This method also predicts a low D/H ratio, but can be accounted for somewhat by a process called 'fractionation', which increases the D/H ratio with time.
Scattering of material by other planetary bodies
The growth and migration of giant planets can cause chaos within a protoplanetary system, scattering and perturbing the orbits of smaller planetesimals. In the case of the Solar System, the growth and migration of Jupiter is thought to be responsible for the inward scattering of planetesimals, trapping them in the asteroid belt. Others were scattered further in, and could potentially have delivered water to the terrestrial planets.
Now, to answer your question... When did the first liquid water settle on planets? Well, the answer is that we don't know, because we still don't know how water was delivered. Finding the answer to this is one of the major ongoing areas of research in planetary science.
For further reading I suggest these two excellent recent reviews:
Oberg & Bergin (2020) - "Astrochemistry and Composition of Planetary Systems"
Raymond & Morbidelli (2020) - "Planet Formation: Key Mechanisms and Global Models"