I don't have hard evidence like studies for you, only personal experience (eastern Germany):
Yes, we do start counting from the thumb. My kids and their friends in Kindergarten do it that way, my colleagues do, my friends and family count like that aswell. In fact my older daughter (5yo) was only today experimenting to count in different ways, and in the end dismissed all the "wrong" ways. I don't know any Germans who don't count like that. My wife, who is a teacher, says she has seen russian migrant kids counting from the index finger, but no Germans either.
The scene in the movie is plausible.
Edit based on the comments: Maybe as a rule of thumb, keeping down only the pinky (on its side of the hand) feels awkward and will be avoided by first prioritizing the thumb (until 3) and then switching thumb for pinky (at 4). Signaling "one" might be done with the index finger if the thumb is not unambigious enough("thumbs up"), but counting will start at the thumb, so there probably should be made a clear distinction between counting and signaling. When counting, the pinky-thumb switch is not done by everybody, as a non representative survey among a couple of locals who happened to be at hand showed just now.
- _lll. or .llll (appears to be 70/30)
- _.... or .l... depending on ambiguity wrt. "thumbs up"
- .ll.. or _l... (appears to be 50/50)
- _ll.. definitely
- .llll definitely
(The ASCII art is supposed to be right hands when looking at their backs, no offense to lefties implied!)