Does static ability from a permanent apply while that permanent is being cast?

Static abilities of a permanent only function when that permanent is in the zone they are written to apply in — for most permanents, that is the battlefield. While a spell is on the stack (i.e., being cast), it is a spell object, not a permanent, and its static abilities do not apply to the game. (CR 112.6, 604.2)

There are narrow exceptions: some abilities explicitly function in other zones, such as cards with abilities that work from the hand or graveyard (e.g., 'you may cast this from your graveyard'). These are specifically called out in the card text. Without such explicit wording, the ability does nothing while the card is on the stack. (CR 112.6a)

This is a common source of confusion because players sometimes expect a creature's replacement effect or cost-reduction ability to apply to its own casting. For example, if a creature says 'Spells cost {1} less to cast,' that ability only functions once it's on the battlefield — it does NOT reduce its own casting cost, because it isn't a permanent yet when you're casting it.

Concrete example: You cast Goblin Warchief, which gives Goblin spells '{1}' less to cast. Goblin Warchief's own static ability is not active while it is on the stack, so it does not reduce its own casting cost. Only after it resolves and enters the battlefield will it start reducing the cost of future Goblin spells you cast.

In summary: a permanent's static abilities 'turn on' at the moment the permanent enters the battlefield (or whichever zone the ability specifies), never earlier during casting. (CR 604.2, 112.6a)