There are several instances in history that are considered to be good candidates as discovery and first use of zero. Examples includes Ancient Sumarian and Babylonian civilizations, Mayans, medieval India, China and Cambodia.
What are the mathematical concepts and ideas that can be logically considered as precursors to discovery of zero. For example, familiarity and extensive use of a positional number system within a civilization could be considered as one such precursor. Another is evidence of experimenting with different symbols like empty space, dot, etc. to indicate absence of a number and need to deal with relatively large numbers.
Similarly what are the ideas that can be anticipated to follow discovery of zero? Here are some examples: negative numbers, new rules of arithmetic to handle zero and negative numbers in addition to natural numbers, etc.