According to this source, pages 378-382 and 406, there were no launch suits for Shuttle missions STS-5 through STS-33. Instead, crew literally wore shirtsleeves during launch and re-entry, plus anti-G pants under their coveralls, and a small helmet called the Launch Escape Helmet.

Since many of these missions had no EVAs, does this mean that some Shuttle missions carried no spacesuits?

training with the Launch Escape Helmet

The Launch Entry Helmet (LEH) was donned via an unusual “clamshell” hinging mechanism that divided the helmet into joinable fore-and-aft, semi-hemispherical sections. [...] The resulting helmet, perhaps unsurprisingly, looked much like a full-pressure suit helmet, but it was not.

p. 378

Launch Entry Helmet

Even worse, the helmet had been previously tested and rejected by both the U.S. Navy and U.S. Air Force.

In reality, the only protection the helmet provided was against ambient noise during ascent, incidental bumping of the head against the inside of the crew module, and possible smoke in the cockpit.

p. 381