Can you cast an instant in response to your own triggered ability before it resolves?

When a triggered ability triggers, it is placed on the stack the next time a player would receive priority (CR 603.3). Once it is on the stack, the active player receives priority first. This means you can absolutely cast instants or activate abilities in response to your own triggered ability before it resolves.

The key rule is CR 116.2b: players may cast instants and activate abilities whenever they have priority. After any object is placed on the stack — including your own triggered ability — priority is passed around, giving every player a chance to respond (CR 116.3). The triggered ability only resolves when all players pass priority in succession with nothing new on the stack (CR 609.1).

This is a fundamental part of the stack system. It doesn't matter who controls the triggered ability; once it's on the stack, the game follows the same priority rules. You are never forced to 'let your own ability resolve' immediately.

Example: You control Goblin Bombardment and sacrifice a creature, triggering its ability to deal 1 damage. Before that triggered ability resolves, you cast Giant Growth on a creature you control (perhaps to save it). Giant Growth resolves first, then Goblin Bombardment's triggered ability resolves and deals its damage.

Note: If the triggered ability itself was placed on the stack as the result of a spell or ability resolving, you still get priority afterward and may respond before it resolves. CR 603.3 and 116.3b confirm this behavior.