Can you tap a land for mana during your upkeep before your draw step?

During your upkeep, you receive priority and may activate mana abilities at any time you hold priority. Tapping a land for mana is a mana ability (CR 605.1a), and mana abilities don't use the stack — they resolve immediately (CR 605.3a). There is no restriction that limits mana production to your main phase.

The turn structure places the upkeep step before the draw step (CR 502.1, 504.1). During upkeep, after the active player receives priority, they can activate any activated abilities, including mana abilities. This means you can absolutely tap a Forest for green mana during your upkeep.

However, keep in mind that mana in your mana pool empties at the end of each step and phase (CR 500.4). So any mana you produce during upkeep will be lost when the upkeep step ends unless you spend it on something during that same step — such as paying for a triggered ability that triggered during upkeep.

Concrete example: You have a triggered ability that says 'At the beginning of your upkeep, you may pay {2}. If you do, draw a card.' When that trigger goes on the stack and you receive priority, you can tap two lands for mana right then and there to pay the {2} cost before the trigger resolves. The mana is produced legally during the upkeep step.