At the moment of death, contrary to what may common assumption, rigor mortis does not set in; at the moment of death „flattency“ sets in, which is relaxation of muscles, not fixation or arrested motion of muscles.
See Wikipedia, Rigor Mortis, Physical changes.
"At the time of death, a condition called "primary flaccidity" occurs. Following this, the muscles stiffen in rigor mortis. (...) Starting between two and six hours following death, rigor mortis begins with the eyelids, neck, and jaw. (...)"
Counterintuitely, and this might be the key to the question, a smile on the face is not produced by relaxing one's muscles. To produce that gesture affords the contracting of several muscles.
There are many search results on "smile muscle contraction" with Bing and Google
Google's first page incidentally tells about Duchenne smile, too (nowadays presumably termed "resting b.... smile"):
"All smiling involves contraction of the zygomatic major muscles, which lifts the corners of the mouth. But a Duchenne smile is characterised by the additional contraction of the orbicularis oculi, (...)."
Whereas, of course, it is literally possible to die with a smile on one's face - this may be a matter of character and circumstances and the ability to apply minimal muscle effort to produce the expression - it should be infered from the above
that from the moment of death to entertain active muscle contractions is no longer feasible.
Hence: No, it is not possible to have a smile on the face after death.
Addendum: Wikipedia, cited above, explains the mechanism of rigor mortis - depletion of ATP, influx of calcium which may be artificially initiated applying cold. I found no sources assuming onset of rigor mortis ("shortening" muscles) produces some smile; and this issue seems not to be addressed by the question.
However, as one comment above suggest, there does exist "Cadaveric spasm" that sets in at the moment of death, thus - in theory - conserving and literally freezing any muscle action at the very time of death, cp.
Wikipedia on Cadaveric spasm:
"... may affect all muscles in the body, but typically only groups, such as the forearms, or hands. Cadaveric spasm is seen in cases of drowning victims when grass, weeds, roots or other materials are clutched (...)"
Almulhim / Menezem, Evaluation of Postmortem Changes, 2021
(easy accessible information on what happens after death in general):
"Rigor mortis needs to be distinguished from cadaveric spasm/instantaneous rigor, which is an immediate contraction of a small group of muscles at the instance of death, seen in scenarios of violent death like in the case of drowning."
However disciplined such smile may be (I remember some movie's title: Drowning by numbers) instantaneous "freeze" seems a rare exception to the rule.