Noise from 2013 tundra 5.7

Hello Master,
My 13 5.7 tundra makes a loud noise when starting cold. Once it made the noise and the truck kept trying to start on its own w/o key being turned, it finally cranked over.
A few years back it had this same noise. After a few visits to my toyota dealer they isolated the trouble to a bad alternator. It was swapped out and the noise went away on cold starts. Now it's back.
Can it be something else?
How does a water pump sound when going out?
Could it be the valves from secondary air pump system?
Any help is appreciated.
Jt

 

Can you describe the noise?

 

Video will help a lot. People are always talking about noises with the 5.7.

 

Sure, I'll have my wife record it tomm morning. I cleaned my battery terminals up as they were covered with corrosion.

 

That's never a good thing.

 

Why can’t it be the alternator again? If it’s doing the same thing as last time.

 

Man his luck. Toyota parts are know to last a long time.