Sorcerers have the easiest ways of explaining their psychic powers. That was just the way that they were born. While it might not make sense to anyone who doesn't have a mind like theirs, they could easily just be born with a modified mind. Another explanation may be through the effects of mind modification accidentally created by Mindflayers.

Wilder

Wilders are an odd creation, even among sorcerers, they have the same magical blood as their peers, but they gain their effects through the mind. Most come from failed illithid experiments, but there have been cases of the odd knock in the head or being mysteriously born with it. No matter where they came from, their true matter is their brain matter.

Wilder Sorcerer Features Sorcerer level feature 1st Alien Mind 6th Psychic Surge 6th Psychic Feedback 14th Id 18th Clarity

Alien Mind At 1st level, your mind becomes so wild that you resist mind altering effects. You gain advantage against mind altering effects and resistance to psychic damage.

Psychic Surge At 6th level, you gain the ability to channel raw emotion into your spells. Spells cast at first level or above can be channeled above your spell maximum by channeling sorcery points equal to half the spell's normal maximum rounded up. For instance, a 6th level sorcerer may Psychic Surge a fireball. Their max spell level is three, so they would have to spend two sorcery points to increase it to a fourth level fireball.

Psychic Feedback At 6th level, you gain the ability to send feedback to those who try to control you. When someone tries to use a mind altering effect or tries to hit you with psychic damage, you can use your reaction to channel sorcery points into the user to harm them. You deal 1d10 psychic damage for each point you channel into them. The points channeled have another effect when channeled, you can add +1 to your save or reduce the psychic damage by 1 for each point channeled into the enemy.

Id At 14th level you can let out the worst recess of your mind. Once per day, when you are lowered to 0 hit points you can heal 1 hit point and have your Id take over for 1 minute. You gain 10 temporary Sorcery points that do not count towards your maximum sorcery points. After the time runs out you loose these sorcery points and any spell slots gained by it. When in this state, you must make a wisdom save DC 15 if you succeed you can use your turn normally, if you fail, you lose control of yourself and try to attack the closest creature. This is controlled by the DM who may decide what you use and how you use it, given spells, weapons, and environment.