Activate Overgrown Estate by sacrificing Arid Archway.
When Arid Archway dies, Toph, Hardheaded Teach triggers, returning Arid Archway from your graveyard to the battlefield tapped.
When Arid Archway enters, it triggers, returning the artifact cast in step 1 from the battlefield to your hand, as it's a land due to Toph, the First Metalbender.
Resolve the Overgrown Estate ability
Repeat.
This ingenious loop turns a zero-cost artifact into an engine of endless rebirth by leveraging Toph, the First Metalbender to permanently blur the line between artifacts and lands. With that foundation set, casting the artifact triggers Toph, Hardheaded Teacher to animate Arid Archway, which you then sacrifice to Overgrown Estate for a steady stream of life. Thanks to Toph, the First Metalbender's static ability making your artifacts into lands, Arid Archway's entry trigger conveniently bounces the artifact right back to your hand to start the cycle anew, while its death triggers a timely return courtesy of the Teacher.