My research was admittedly incomplete, so I missed an early example: "Polly and Her Pals" -- Wikipedia entry here.
Polly was the work of Cliff Sterrett (1883-1964), considered by some as "cartoonist's cartoonist" --- the best of the best in that trade. His Wikipedia entry mentions Li'l Abner cartoonist Al Capp stating: "Now, Sterrett—that's the guy who was the greatest." His style became increasingly Modernist, as I posted here.
This Lembiek post mentions something neither I nor the Wikipedia writers knew:
"Because of arthritis, Sterrett was forced to hand over most of the art duties during the 1930s. The daily 'Polly' strip was handled by his assistant Paul Fung from 1935 until the end of its run in 1942. Sterrett continued to supervise and occasionally draw the Sunday page until his retirement in 1958. The final episode of 'Polly and Her Pals' was published on 15 June 1958. Other ghost artists that worked for Sterrett were Vernon Greene, John Kowalchik, Fred Schwarze and Bob Dunn."
Ghost or assistant comic strip artists were more common than most folks realize. An important example is the famous fantasy illustrator Frank Frazetta who spent several years ghosting for Al Capp. The best ghosts mimicked the strip creator's style almost exactly, so all the artwork in the Gallery below can be treated as Sterrett's.
As for the title of the present post, I cannot absolutely vouch that Sterrett always drew Polly's head in profile. That said, none of the Polly panels I noticed on Google showed her any other way. Below are some Polly snippets illustrating that point. Click on them to enlarge.
First, an example of a Sunday panel minus coloring that shows Sterrett's mature style. Note that Polly does not appear in the action that features Paw, her father (though she can be seen in the title block). As Wikipedia notes, he soon became the star of the strip.
This extract from a Sunday panel appeared when the strip was about one year old. Polly is shown in profile, though the most of the dancing ladies have full or partially full faces. I have no idea why Sterrett didn't do that with Polly.
An out-take from later that year with five views of Polly, all with her head in profile.
Same story here.
Twenty years after Polly's debut. Her body posing before a mirror is not in profile, but her head is, for practical purposes.
Sterrett made sure Polly had fashionable clothing and hairdos. But her blonde 1934 hair is now brown. And she's in profile, even in the header above the panel extract.
A late example, Polly in profile at the left. Note Paw and his Modernist cat, "Kitty."