Engine rattle at cold start

assuming the problem isn't internal, check all of the pulleys associated with the serpentine belt.

Does this vehicle use lots of engine oil?

I think you have to check your oil control solenoid, sometimes when they are weak they can't hold the oil. It let the oil escape from the vvt actuator which supply oil to the cams. So when you starts the car, the cams have to wait for oil from the oil pump to lubricate the cams

It is probably SB No. T-SB-0146-10 http://media.fixed-ops.com/Toy_ServiceBulletins/sb0041t13.pdf

How is it no one has a solution for this!!! My car has this same problem. What gives... How do we fix this?

My 2016 with 42k miles does this the first half second. Not worried. Probable chain rattle until oil gets to it. Old Corolla 2 TC/3 TC pushrod engines did this. If rattle persisted more than a few seconds (usually with hugely advanced mileage), then plan on a chain kit.