The word "develop" has applied to projects longer than we've had computers. Merriam-Webster has the definition "to create or produce especially by deliberate effort over time". Computer programs require this kind of work, so the word fit.
Google Ngrams shows a huge spike in the use of the term "research and development" around WWII. I'm having trouble linking it, but you can easily reproduce the search.
The earliest example I found of the term applied to computer programming is a chapter called "The Program Development Cycle" in Spencer's "Introduction to Information Processing" of 1974. The chapter is full of italicized key terms (instructions, program, flowchart), but "development" is not given this treatment. It wasn't yet a term of art, just the word for a process of creation.