The most believable path isn't about armies or gold at the start, it's about narrative. A conqueror from a fallen state has one asset left: a story. The story of loss, of a rightful legacy stolen. They must become a symbol, a living myth, before they can command soldiers. Look at how many romantasy or epic fantasy series handle this—the exiled prince or queen doesn't just show up with a sword; they gather believers. They perform acts of calculated, public defiance that get whispered about in taverns. They find a prophet or an ancient text that lends divine weight to their claim. The power is rebuilt in the minds of the people long before a single castle is taken.
Materially, they'd seek a patron, but never as a mere mercenary. The deal would be a marriage alliance, or a pact to defeat a mutual enemy, framing it as an equal partnership even when they have nothing. Their inner circle would be tiny, built on unshakeable loyalty forged in the ashes of the old kingdom, not hired. The real trick is transitioning from a story to a state. That's where so many fictional versions stumble or become tyrannical—they get the crown back but can't remember how to rule a living country, only how to conquer a symbol. The rebuild is hollow if it's just a revenge plot.