Getting the "first" element of a JSON object expression is difficult, since JSON objects are not intended to be ordered collections. They are "ordered" in JSON only because they must have a string serialization that is an ordered sequence of characters, but two JSON object expressions with differently-ordered properties are meant to convey identical semantics.
If you are willing to trust your JavaScript environment to preserve the ordering of keys when iterating (which is not an assumption defined in the ECMAScript spec, but may be true in your environment's implementation), you can do:
var myObj = JSON.parse("{ ... }");
var firstKey = Object.keys(myObj)[0];
delete myObj[firstKey];
If you do not want to make such an unsafe assumption, you need to read the JSON string and manually determine the key name between the first set of quotation marks. This involves some effort, because you must also handle escaped quotation marks that may appear within the key name itself.