There were also minimalist SQL interfaces to say BerkeleyDB and DBM around.
It was a rival of MySQL for a while. The article says "mSQL was the first low-cost SQL-based database management system" but notes citation needed. Certainly matches my memory though.
Interbase is still around and it can store the entire database in a single file or across multiple files. There are also 3 versions of it available: IBLite (in process DB engine), IB-To-Go (in process DB engine), and Interbase (server based).
That said, I'm not aware of anyone doing that with SQL before SQLite. Though I might well have missed some.