"A lot of the behaviour and the personality is much more relatable than we want to admit," said the Hollywood star, who has won critical acclaim for his uncanny performance.
The film, which premiered at the Cannes Film Festival, has drawn huge controversy and legal threats from the ex-president, particularly for a scene in which Trump is shown raping his wife.
But much of the film portrays a younger Trump as a nervous, naive outsider from New York's outer boroughs, trying to find his way in a cut-throat and elite Manhattan world he knows little about.
It is an approach sure to surprise, or even anger, anyone expecting or wanting a left-wing political hatchet job.
For Stan, who was born in Communist Romania and did not move to the United States until he was 12, that sense of Trump striving to belong resonated.
"My mother told me that I had to become somebody," he told AFP in an interview.
"There was a lot of shame, when I grew up, coming from Romania... 'don't tell people' and 'blend in.'"
The 41-year-old Stan has rocketed to fame in recent years, in large part due to his role as the Winter Soldier in a number of record-breaking Marvel superhero films.
But Stan drew parallels between his mother's message, and the intense pressure put on Trump and his brothers by their brutally tough father Fred.
As the film starts, Donald Trump is failing to convince his father that he can pull off a daring hotel deal.
Instead it is Roy Cohn, a formidable lawyer with powerful political connections, who believes in the young property developer, taking him under his wing.
While Trump is initially queasy about Cohn's willingness to "violate a few technicalities", he quickly adopts and even surpasses his mentor's embrace of the dark arts in pursuit of fame.
The movie shows how "anyone that grows up in America" can be corrupted by a capitalist society that rewards greed, ruthlessness and ambition, said Stan.
"Nothing is ever good enough. You look at people achieving things, but there's always more, you've got to have more," he said.
'Hardest scene'
Stan prepared for the role by devouring magazine interviews, watching videos and obsessively listening to audio of Trump from the late '70s and early '80s.
He would listen "non-stop," whether driving, walking, shopping or even "on headphones in the bathroom."
Stan tried to avoid the many "Saturday Night Live"-style parodies of later-era Trump, noting that "you just had to put the noise away."
The role calls on Stan to gain weight as the years progress and he "tried to eat as much as I could" before certain shoots. Because not everything was shot in sequence, other scenes required prosthetics.
And then there is the much talked-about rape scene.
It occurs after an argument, in which Trump's first wife Ivana belittles him for growing fat and bald.
In real life, Ivana accused Trump of raping her during divorce proceedings but later rescinded the allegation.
Stan said preparing for that scene did not particularly trouble him.
Instead, "the hardest scene, that I was always afraid of", was another in which Trump mourns the loss of his older brother Freddy, an alcoholic who died aged 42.
Trump is shown genuinely caring for Freddy as well as Ivana, before his humanity is eroded by the power and wealth that devours him.
"It's interesting how much we don't want to remember about him," said Stan.
