The origins of her powers are presently unknown, so in that sense that's all that can be said about your question. She's known to have had them since a young age, if not since birth. Her sister also has exceptional power, but Tatsumaki's is just so ridiculous that she puts it to shame. So possibly she is just the winner of the psychic genetic lottery. We do know there is some organization that was trying to engineer and refine psychics, ultimately including Tatsumaki, but to date Tatsumaki's connections to them are not known to predate her childhood.
As a storytelling matter, the entire character and power level of Orochi (and Orochi-Psykos) were specifically designed to challenge Tatsumaki. In the original webcomic, Tatsumaki is never really challenged at her full power during the MA arc, and she still pulls the entire base up from underground with barely any effort and tries to take everyone on by herself. Instead she gets hit with a cleverly orchestrated sneak attack that gives her a concussion, which significantly dampens her power. At the very least, Tatsumaki herself blames everything on it, rather than anyone actually having adequate power to oppose her.
For the manga version, Murata and One decided that Tatsumaki needed a more proper challenge and a more breathtaking display of her power. Hence the Orochi-Psykos fight and all the ridiculous stuff Tatsumaki does during it. This also serves to help them introduce a number of elements about Tatsumaki's backstory and motivations earlier than they are given in the webcomic. It also elevates the concept of a "God" level threat from unrealistic bluster and exaggeration to plausible. As a matter of storytelling tautology, a "God" level threat must necessitate the world be able to sustain and produce heroes of great power to oppose it, and so a Tatsumaki like entity is an inevitability.
Back to the in-story reasons, the best we can do is conjecture, as there are quite a lot of questions about Blast, the nature and origins of his power, and what exactly these cubes are he's collected and who the "him" he says it connects to actually is. These mysteries seem to be going down into the very roots of the nature of this world, and may be near cosmic in profundity (and so make the idea of a "God" level threat potentially more than just bluster and exaggeration), so any further revelations about them may similarly reveal the reason that certain heroes, Tatsumaki and Blast in particular, exist and have so much power.