Get the index of an element inside queue c#

Maybe a List or an Array would be better for such actions but you could try this:

queue.ToArray().ToList().IndexOf(email);

You can use extension method, something like:

public static int IndexOf<T>(this IEnumerable<T> collection, T searchItem)
{
    int index = 0;

    foreach (var item in collection)
    {
        if (EqualityComparer<T>.Default.Equals(item, searchItem))
        {
            return index;
        }

        index++;
    }

    return -1;
}