Every US-market engine offered in the Toyota Corolla is chain-driven, so there is no timing belt to replace and no interval to budget for.
No replacement interval - this engine uses a timing chain, not a belt
Timing chains are designed to last the life of the engine and carry no scheduled replacement interval. If a shop quotes a "100k mile timing belt service" for this vehicle, that is a quote for a part it does not have. On this model 1ZZ-FE, 2ZR-FE/2ZR-FAE and M20A-FKS are all chain-driven. This covers US-market engines - overseas versions of some of these models were sold with belt-driven diesels, so if yours is an import, go by its own handbook.
A chain is not a lifetime part in the sense people assume - it is a part with no scheduled interval, which is a different thing. Chains stretch as they wear, and the plastic guides and hydraulic tensioners that keep them tight are usually what fails first. The symptom is a rattle from the front of the engine for a second or two on a cold start, sometimes with a timing-correlation trouble code (P0016 / P0017). That is worth investigating, not ignoring. What does not follow is replacing a healthy chain on a mileage schedule: there is no interval to follow, and clean oil changed on time is the only thing that measurably extends chain life.
The factory schedule for the Toyota Corolla contains no timing belt replacement, because the engine does not have a timing belt. That is a complete answer to bring to the conversation: not an accusation, just the schedule.
Before assuming the worst, check what the line item actually says. The accessory drive belt - the serpentine belt that runs the alternator and, on many engines, the water pump or the A/C compressor - is a real wear item on this vehicle, and "drive belt" and "timing belt" get shortened to the same word on both sides of the counter. A quote to replace a cracked serpentine belt is legitimate. A quote to replace a timing belt is a quote for a part that is not there.
The factory schedule is one input, not a verdict on your shop. Wear items do fail early, and somebody looking at the car can see things a schedule cannot. What the schedule settles is whether a service is due - which is the part you could not check for yourself until now.
All maintenance schedules - timing belt or chain, model by model