Not sure what you call it, a whistle or a whine. But 7.3 PSD’s and older Dodges have a turbo whine out the tail pipe at idle and acceleration. My Yanmar diesel in my does the same thing when flushing the engine on the trailer. You just have to know what the sound is to notice it.
Now you say it whistles loud at start and goes away. Does it do it when it’s a cold start, warm start, or both? Does it whistle like boost or exhaust is leaking out a gasket causing a whistle like a ref uses on a sports field or a specific noise like a whine out the exhaust pipe or intake?
Some other thoughts.
1) If you give the truck throttle when starting that is going to spin the turbo. That may change the whine pitch.
2) Maybe you have a exhaust leak and it whistles, things get hot and it seals up.
3) Your truck has a cold in advance and high throttle soleniod. So our trucks run different cold than minutes later hot.
Maybe post a Video on Youtube for us to hear it.