Can you cast spells during your opponent's upkeep step before their upkeep triggers go on the stack?

When the upkeep step begins, the active player (your opponent, in this case) does not immediately receive priority. Instead, any triggered abilities that trigger 'at the beginning of upkeep' are first placed on the stack per CR 502.6 and CR 405.5. Only after all such triggers have been put on the stack does the active player receive priority for the first time in that step (CR 116.3b, CR 502.3).

This means there is no window in which you can cast a spell or activate an ability before upkeep triggers go on the stack. The game never offers either player priority at the very start of the step — triggers are collected automatically as a state-based-like process, and priority is only granted afterward.

Once the upkeep triggers are on the stack and your opponent receives priority, they may pass priority to you. At that point, you may cast instants or activate abilities in response to those triggers, before they resolve.

Concrete example: Your opponent controls a Sagas or a 'Dark Confidant' that triggers at the beginning of their upkeep. You want to destroy Dark Confidant before its trigger occurs. You cannot do this — the trigger goes on the stack automatically, and only then does your opponent get priority. You may respond to the trigger on the stack, but you cannot prevent it from being placed there.

Key rules: CR 502.3 (upkeep step structure), CR 116.3b (active player receives priority after triggers are placed), CR 603.3 (triggered abilities go on stack when their trigger event occurs at the start of a step).