You might say, "The first step towards organizing the prevailing disarray in the archives was the formation of the X Committee in 1835." To me "organizing the disarray" means to reduce, or eliminate disorder. However "systematize the disarray" means to take steps to ensure that disorder happens regularly or all the time (i.e., systematically).

To systemize disarray sounds weird to me. I would say "The first step towards systematization and dispelling prevailing disarray in the archives was the formation of the X Committee in 1835.

I would add an article ('a' or 'the') before 'prevailing'. It depends a little on context which is preferable, but my own choice here would be 'the'. "The first step towards systematizing the prevailing disarray in the archives was the formation of the X Committee in 1835."

The first step towards systematizing the prevailing disarray in the archives was the formation of the X Committee in 1835.