Priority is tricky to nail down e.g. the EDSAC was operational a year before the Mark 1 (which actually was not operational until 1949). Because of the "B" Williams Tube which held the two index registers of the Mark 1, many other manufacturers -- e.g. Burroughs -- later called their index registers "B registers". (Also, I think the Univac I and II were successful commercially, and earlier than the 704.)

I started programming in earnest and for money in 1961 mostly in machine code on a variety of machines, and I'm pretty sure that the notions of single dimensional sequential locations of memory as structures (most often called arrays, but sometimes called lists), predated the idea of index registers. This is because I distinctly remember being first taught how to move through arrays sequentially just by direct address modification -- this was called indexing in the Air Force -- and later being introduced to the index register or registers -- depending on the machine.

My strong guess (from above) is that the array as sequential memory accessed by address modification of some kind was a primary idea in the very first useful computers in the late 40s, and that this idea pre-dated index registers.

It would be well worth your time to look at the instruction set of EDSAC, and try writing some programs.