Who were the first people to lose their lives on the Titanic?

There is no way of telling. That "Special" that you saw used "journalistic licence" (they made it up). This goes to show things never change as the newspapers were reporting "no casualties" or "casualty lists" about the Titanic before anything was actually known in Britain or America. Your theory makes as much sense as theirs, and is probably closer to the truth as the water tight doors had been closed, trapping many in the engine/boiler rooms.

Looking at the plans, the mail room was on the lower deck, at the same level as one Third Class Deck, and below another. Given that there are many reports of gates being locked to prevent Third Class mingling with Second Class during the voyage, AND the assertion that they were also locked to stop overcrowding and panic in the stairwells, then it is unlikely that anyone who DID get out of the mail room would be able to return. The engine room was two decks below this, and would have flooded first, drowning those working there.

Yes it would have been Stokers , Greasers , Engineering personal , as these would have been located well below the water line , and the boilers would have had to been drawn ( fires out ) steam released so the boilers did not explode , these men remained at their posts until ordered to leave , many never made it .

Your very intelligent answer is as good as anyone else's. Fact is, despite 100 years, thousands of people and countless hours of research, some things will forever belong solely to Titanic's dead.

There is no right answer to it, because no one know the truth who were the first people lose their lives on Titanic,

I don't think it was Leonardo DiCaprio.