Use a TimeSpan

using System;

public static class Gigasecond
{
    public static DateTime Add(DateTime birthDate)
    {
        return birthDate + TimeSpan.FromSeconds(1_000_000_000);
    }
}

The DateTime class supports adding a TimeSpan instance via the + operator. We then simply use the + operator on the DateTime instance and pass it the gigasecond in the form of a TimeSpan by using its TimeSpan.FromSeconds() factory method. This will return a new DateTime instance with the amount of seconds represented by the TimeSpan added to it.

Shortening

There are two things we can do to further shorten this method:

1. Remove the curly braces by converting to an expression-bodied method
2. Replace 1_000_000_000 with 1e9, which is the same number but in scientific notation

Using this, we end up with:

public static DateTime Add(DateTime birthDate) => birthDate + TimeSpan.FromSeconds(1e9);