That’s the usual story, but a look at the recording chronology as detailed by Lewisohn suggests the Beatles didn’t really begin Sgt Pepper in earnest until after “Strawberry Fields Forever” and “Penny Lane” had already been recorded and earmarked for a single.
After completing Revolver in June 1966, the Beatles took a five-month break from the studio. They don’t seem to have spent much of the time writing new material: upon returning to the studio in late November, they spent a month working on just two songs*: “Strawberry Fields Forever” and “When I’m 64,” the latter being a reworking of a song Paul had written years earlier. Once these were finished, at the end of December, Paul brought in “Penny Lane,” which they worked on for the next three weeks. It was evidently decided before the track was even finished that this would be one side of the new single, as a mix was prepared to ship to Capitol in the USA the same day the final overdubs were recorded.
With “Penny Lane” in the can, the Beatles spent two days on the basic tracks for “A Day in the Life,” but recorded nothing else in the last half of January. All of the remaining Pepper songs (plus “Only a Northern Song”) were recorded in the two-month period from February 1 to April 1, 1967, with some overdubbing and mixing continuing over the following three weeks. So even though the Beatles were technically working on Pepper material as far back as November 1966, Pepper as an album project didn’t really exist until February 1967.
*Not counting the 1966 Christmas record, which was thrown together in a day during this period, or the improvised freak-out “Carnival of Light,” which was likewise tossed off in a single session.