Generally, see CMOS's great advice on the issue:
Q. Is it necessary to use a comma after words like next, then, after
that, last, and finally when they are the beginning of a sentence? I
am a lower-school teacher and need to clarify this.
A. Punctuation is not so simple that you can make a rule that a comma
“always” follows a given word or phrase. Commas depend on syntax as
well as pacing, tone, and personal preference. Two examples with next:
Next comes the scene where he buries the toenails.
Next, since he was still breathing, she worked a crossword puzzle.
Please don’t teach your students punctuation until you understand
this. Find a grammar book and read the punctuation chapter. CMOS is a
good place to start.
Advice has varied for centuries.
See, in this specific example:
; then they sold it for considerable profit.
Do not place a comma after Then
Commonsense Grammar And Style
By Phillip S. Sparks
This is a fight fought even by the editors of John Donne:
Then, lest thy love, hate, and me thou undo
where some editions skip the comma after "Then"
as shown, e.g., in this annotation:
The Songs and Sonets of John Donne - Page 164
John Donne, Theodore Redpath - 2009
Now, let's get to some stats.
FYI, at COCA (CORPUS OF CONTEMPORARY AMERICAN ENGLISH):
. THEN ,
Thus, while the starting "Then"s without a comma represent a majority, those followed by a comma are around in quite representative numbers.
These are two examples from perhaps the greatest American writer:
Her mother died first. She said, “Take care of paw .” Lena did so.
Then one day her father said, “You go to Doane’s Mill with McKinley.
It required only one or two questions . Then, sitting on the top step,
the fan and the bundle upon her lap, Lena tells her story again, with
that patient and transparent recapitulation of a lying child, the
squatting overalled men listening quietly.
Light in August, by William Faulkner
showing Faulkner feeling the need for both approaches.
But there is no comma after starting "Then," in "V." a large novel by Thomas Pynchon, and he is great too, IMHO :-)
To a large extent, I feel this is about pauses in speech, and about how breezy/fast a flow a writer desires/designs to have.