My truck makes this exact noise at the exact sound level. I believe it is a lifter issue it does it on a 95 degree day just as much as a below 30 degree morning, if the truck sits for about 4 hours it does it on a rare occasion it does not. It last around 2 to 3 minutes and fades until it has reached 190 minimum. If I wind the gear out to about 2500 rpm there is a constant lifter rattle. At idle in a drive through I can hear a faint lifter tap no matter how warm the engine. Dealer says if I pay for the tear down and they find something they will fix it, if not I'm out the tear down and reassemble $$.
youtu.be/4lxjdaOv9qE