That isn't possible. Beginning of upkeep ins't a phase, it's a trigger. So the triggers have already occurred, so you're right.
Just to clarify further on what 49 cents said, here's the relevant rules sections:
303. Upkeep Step
303.1. As the upkeep step begins, any abilities that trigger at the beginning of that upkeep step and any abilities that triggered during the turn’s untap step go on the stack. (See rule 410, “Handling Triggered Abilities.�) Then the active player gets priority and players may play spells and abilities.
410.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability triggers. When a phase or step begins, all abilities that trigger “at the beginning of� that phase or step trigger. The ability doesn’t do anything when it triggers but automatically puts the ability on the stack as soon as a player would receive priority. The ability is controlled by the player who controlled its source at the time it triggered. It has the text of the ability that created it, and no other characteristics.
So by the time either player has priority (i.e. to discard using Tog), the "beginning of upkeep" triggered abilities are already on the stack (meaning more can't go on because "beginning of upkeep" has passed).