The intake camshaft pulley has a mechanism called VVTi used to vary cam valve timing.

This engine model has had issues of this mechanism making noise from lack of engine oil pressure at engine start up. Reasons being the oil system design plus a possible plugged oil filter screen to VVTi unit.

The result is two major parts bang against each other like an impact wrench socket bangs on a bolt. This banging over time can cause the bolts holding the unit together to loosen and then fail. The result would major engine damage.

Would caution against driving the car until someone removes the valve cover and inspects the VVTi for damage. The system is at the top of the engine, passengers side, near intake manifold.

If it is the VVTi, the fix can be very expensive.

Search the net on 2AZFE VVTi noise. Toyota had a service bulletin on this but your car is past this warranty repair.

Also check for engine oil sludge which would plug everything up.