[@olcharlieboi]

Hmm. Perhaps Rust Warrior gave Asahi a sort of burnt out version of his father's arc reactor, after he self destructed? Rust Warrior would claim that it's useless now, so much that his quirk (which allows him to control machines) doesn't work on it because it's so borked. However Asahi knows he lying and that with a lot of hard work in between jobs, school, and making the exoskeleton, he manages to get the old arc reactor into a semi serviceable order.

And if your wondering why Rust Warrior would give Asahi something as important as the power supply to his villain father suit, it's because Rust Warrior doesn't believe in "sins of the father" and believes that Asahi can do right where his father did wrong. Taking everything away from Asahi would just prevent him from properly making use of the boys talent, or worse make him inherit his fathers grudge and force Asahi into shadier business just to try and do what his father once did. 

Not the whole go mad with power and wreck the city bit. But making mech suits.