Can you take actions during the untap step before permanents untap?

The untap step is special because no player ever receives priority during it. Under CR 502.3, the active player's permanents untap, and then the step simply ends — there is no window for either player to cast spells, activate abilities, or take any other game action during this step.

This is different from most other steps and phases, where priority is passed around and players can respond to things. Because priority is never granted during the untap step (CR 502.4), you simply cannot 'do anything' before untapping happens.

Triggered abilities that trigger during the untap step are held and only put onto the stack once the next step (the upkeep step) begins and priority is first granted, per CR 503.1 and CR 117.5. So even if something technically 'triggers' during untap, it won't resolve until upkeep.

Concrete example: You control a creature with a tap-activated ability. At the start of your turn, you cannot activate that ability before your untapped permanents untap — the untap step offers no opportunity to do so. You must wait until at least the upkeep step, when you first receive priority.

There are no conditions that change this: no player, under any normal game rule, receives priority during the untap step (CR 502.3, 502.4).