The validity of an index depends on the items it includes, rather than anything about standardization and normalization. If the items in your index have an obvious relationship to the concept that you claim your are measuring, then you can rely on "face validity," which basically means that you expect your readers to accept the content of the index without question (in that case you would usually not even refer to validity).

Alternatively, if you want or need to go beyond face validity, you will need to show properties such as "convergent validity" where your new measure correlates with other things that are similar to it.