Cast Temporal Manipulation by paying 3, granting you an extra turn after this one.
Cast Mystic Reflection by paying 1, causing the next creatures or planeswalkers to enter the battlefield this turn to enter as copies of Archaeomancer.
Cast Sram's Expertise by paying 2, creating three token copies of Archaeomancer and allowing you to cast a card with mana value 3 or less from your hand without paying its mana cost.
Each of the Archaeomancer's ETBs trigger, returning Mystic Reflection, Temporal Manipulation, and Sram's Expertise to your hand.
Repeat.
By casting Mystic Reflection before resolving Sram's Expertise, you completely rewrite how the resulting tokens enter the battlefield, turning all three Servo artifact creature tokens into fresh copies of Archaeomancer instead. Each of those new Archaeomancer enters-the-battlefield triggers then fires off to reclaim the very spells you just cast, letting you loop Temporal Manipulation for infinite turns. Sram's Expertise also conveniently supplies a free spell cast during the setup, making this intricate multi-card sequence surprisingly efficient.