Can you cast a spell during the untap step?

During the untap step, neither player receives priority (CR 502.3). Because casting a spell requires a player to have priority (CR 117.1), it is impossible to cast any spell during the untap step — not instants, not spells with flash, nothing.

Priority is the system that controls when players may take actions. It is only passed around and received during steps and phases where the rules explicitly grant it. The untap step is one of the few steps where priority is never granted at all; the others include the cleanup step under normal circumstances (CR 514.3).

The untap step exists solely for the game to untap the active player's permanents (CR 502.1–502.2). No player actions are permitted until the upkeep step begins and the active player receives priority.

Example: It is your turn and you want to cast Opt (an instant) as early as possible. Even though Opt can be cast at instant speed, the very first moment you can cast it is at the start of your upkeep step, once you receive priority — not during the untap step.

This rule applies equally to activated abilities and triggered abilities going on the stack: triggered abilities that trigger during the untap step are held and only placed on the stack once a player receives priority in the upkeep step (CR 503.2).