Does the Oort cloud exist? If so, why can't we see it?

Let's start by discussing what the Oort Cloud is and isn't.

First of all, the cloud is thought to exist; although hard evidence will be hard to come by, the theory sheds light on a number of astronomical mysteries, such as the origin of long-period comets and how best to characterize their orbits.

This region, which is a spherical shell and begins about 2,000 AU (Astronomical Units) from the Sun (to put that into perspective, 1 AU is the average distance from Earth to the Sun, Pluto is 40 AU from the Sun) and extends well out towards the closest star (perhaps as much as 100,000AU away from the Sun or roughly 1/4 of the distance between the Sun and the closest star), according to https://tutor.hix.ai It is a region of space that surrounds the solar system and contains ice, rock, and the occasional larger body, sometimes referred to as Dwarf Planets.

It's not a cloud in the Earthly sense, which are big, puffed objects composed of water vapor that are visible in the sky; clouds in astronomy are much less dense but much more expansive, allowing us to see them when interfering light from stars and galaxies is obstructed.

What then would make it difficult to see the cloud?

Only when we are able to see something can we consider it to be observable in space.

So what does light require in order for something to be visible?

And where does the light come from? It either comes from the object itself (the Sun, a lamp, etc.) or it comes from the object's reflection (the Moon, for example).

The Moon absorbs some light and what is reflected is scattered off in all directions - only a fraction reaches Earth. This is why, despite the Moon's ability to be quite bright at night, it is not nearly as bright as the Sun. When light is reflected, all of the light that strikes the object does not bounce back; instead, it gets scattered, absorbed, and the like.

In contrast, the Oort Cloud has no light source of its own, so whatever light it receives when scattered doesn't return to Earth but instead flies off in random directions. This is why clouds in the Earth's sky are visible: the Sun is a powerful light source that allows clouds to scatter light and yet have plenty left over for us to look up and see them.

The Oort Cloud is not a source of light; instead, light must be reflected from it. Because the Cloud is composed of tiny rocks and ice fragments separated by enormous distances, the majority of light that reaches it is absorbed by the rocks in the Cloud. Because space rocks and ice are notoriously "dirty"—that is, covered in a dark-colored substance known as "space dust"—most light that reaches them is passed through and never reflected.

The only other means of seeing the Cloud is through the use of a deep space probe; however, due to the great distances involved, it is challenging to design a spacecraft that can make the journey. Voyager 1, our fastest and furthest-traveling probe, was launched in 1977; it will take another 300 years for it to reach the Cloud, at which point it will run out of fuel and be unable to explore or return data. Other probes that are leaving the solar system will also run out of fuel well before they arrive at the Oort Cloud.

Based on the radioactive decay of Uranium 238 to Lead, and assuming that astroids containing Uranium 238 started out with 100% Uranium, the age of the rock can be calculated, the solar system is thought to be roughly 4.5 billion years old. The astroids commonly contain about 50% lead, giving a half life of 4.5 billion.

Comets, on the other hand, have an observable life of 5,000–10,000 years. Since astroids and comets are thought to have formed simultaneously during the early stages of the solar system, comets must be 4.5 billion years old.

A cosmic object passing through the Oort belt can dislodge a comet, causing the comet to then enter the observable solar system. As the comet made of frozen ice and dust orbits closer to the sun, the comet evaporates in thousands of years. According to the theory, a vast reservoir of comets exists outside of the observable solar system. The Oort cloud is proposed as an explanation for how comets can be observed to decay and disappear in thousands of years when comets must be billions of years old according to the nebular theory of the formation of the universe.

The solar system would be thought to be only tens of thousands of years old based solely on comet observations, but the Oort belt is a theoretical concept that explains the contradiction between the observations of the age of the comets and the observations of the radioactivity in astroids as well as the theory of the nebular hypothesis of the solar system's formation.

Indeed, the Oort Cloud is thought to exist. It is made up of icy objects at the very edge of our solar system, and because of its extreme distance and the faintness of its constituent objects, it is difficult to observe directly.