Activate Bloodflow Connoisseur 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 Bloodflow Connoisseur ability
Repeat.
This intricate loop turns your cheap artifacts into a recurring engine by leveraging Toph, the First Metalbender, whose static ability reclassifies all your nontoken artifacts as lands. Once that foundation is set, casting a free artifact triggers Toph, Hardheaded Teacher to earthbend Arid Archway into a creature, allowing you to feed it to Bloodflow Connoisseur's sacrifice ability. Because Arid Archway is simultaneously a land and a creature, its death triggers Toph, Hardheaded Teacher's safety net to bring it straight back to the battlefield, where its enter-the-battlefield ability safely bounces your original artifact back to your hand to restart the cycle.