Can you respond to your own triggered ability before it goes on the stack?

Triggered abilities do not go on the stack the instant their trigger condition is met. Instead, they are placed on the stack the next time a player would receive priority — typically at the beginning of the next step or phase, or after the current spell or ability finishes resolving (CR 603.2, 603.3).

Once a triggered ability is placed on the stack, the Active Player (AP) receives priority first (CR 117.3b). At that point, all players — including the controller of the triggered ability — may respond by casting spells or activating abilities before it resolves. So you can respond to your own triggered ability, but only after it has been placed on the stack, not before.

You cannot 'jump in' between the trigger event occurring and the ability being placed on the stack because no player receives priority during that window. The game simply queues the trigger and waits until the appropriate moment to put it on the stack (CR 116.5).

Example: Your creature with Lifelink deals combat damage, triggering a separate ability that says 'Whenever you gain life, draw a card.' That triggered ability is queued, and after combat damage is fully handled, it is placed on the stack. Only then can you (or your opponent) respond — for instance, by activating an ability or casting an instant — before the draw trigger resolves.

In summary: you cannot interact with a triggered ability in the window between when it triggers and when it is placed on the stack. Your earliest opportunity to respond is after it appears on the stack and priority is passed (CR 603.2, 117.3b).