The behavior of electrons in an atom is indeed described by quantum mechanics, and they exist in what are known as quantum states or orbitals. However, it is important to note that the concept of an electron being "everywhere around the proton at the same time" is not an accurate representation of its behavior.
In quantum mechanics, electrons are described by wave functions that determine the probability distribution of finding an electron in a particular region of space. These wave functions are often visualized as electron clouds or orbitals, which represent the regions where the electron is most likely to be found.
When you touch a solid object, such as a table, the atoms in your finger come into close proximity with the atoms in the table. At this scale, the electron clouds of the atoms repel each other due to the electromagnetic force. This repulsion arises from the quantum mechanical interactions between the electrons and the positively charged nuclei (protons) in the atoms.
The repulsive forces between the electron clouds of the atoms prevent your finger from passing through the table. This is because the electron clouds effectively "push back" against each other, creating a barrier that gives the solid objects their rigidity.
So, while electrons do exhibit quantum behavior and have wave-like properties, they do not exist simultaneously everywhere around the proton. Rather, their behavior is described by probability distributions that determine their likely locations in the vicinity of the nucleus.