The first real 32 bit systems where Unix, VMS and Linux. Noboday needed a desktop in those days but anyway X11 was developed.
To be clear, I'm taking about full blown desktop operating systems, not command line interpreters and such. VMS was for minicomputers only. "Linux" wasn't an operating system; it was the development of a kernel built from scratch, modeled after Unix. The earliest distro's were attempts to build an OS around the Linux kernel, incomparable to Unix and OS/2 at the time. The first more mature desktop OSs with a Linux kernel didn't arrive until the late 90s.
I'm not 100% familiar with the history of 32 bits Unix, but I do know that Unix and OS/2 were competing from the very beginning with regards to 32 bits capabilities. I used OS/2 at the time, and yes, there definitely was the need for a graphical desktop or Apple, IBM and Microsoft wouldn't put so much effort in the late 70s and 80s in developing a graphical UI to make things so much easier for office and graphical industry use.
Anyway, Wikipedia confirms the competition between Unix and OS/2 32 bits capabilities, as we can read: "the introduction of the 32-bit Intel 80386, caused Unix to "explode" in popularity for business applications; Xenix, 386/ix, and other Unix systems for the PC-compatible market competed with OS/2 in terms of networking, multiuser support, multitasking, and MS-DOS compatibility."
Atari ST and Amiga. 5 years before Windows 3.1 and even more before OS/2 (OS half).
Are you talking about GUI or 32 bits development? Because Windows 3.0 and 3.1 was just a graphical shell over a 16 bits OS. The very first to develop a GUI I think was Xerox in the early 70s. But that's quite a leap to the 32 bits desktop OSs of the early and mid 90s.
If I'm not mistaken, none of the computers at the time such as the Motorala 68k in the late 70s were 100% 32 bits capable as they still had 16 bit data bus addressing. It wasn't until 1985-1986 with the introduction of the 386DX (which were very expensive at the time) that OSs could be developed to fully run in protected mode allowing 4GB memory adressing. Even in 1995 I could tell the difference between OS/2 and Win95 desktop/multi-tasking performance. OS/2 was clearly superior and much more stable. But IBM wasn't good at marketing and as a result the three main desktop OSs in use since the late 90s are Mac, Linux and Windows.