I've never seen such a CD, but the track you mention must be the gap of track 1 (between indexes 00 and 01, the so-called 'pregap' or just 'gap'). This 'gap' is not played, unless you rewind to time zero and below, just as you describe.
(you can also check this by detecting gaps with EAC and see how long the first gap is - 2 seconds is an ordinary pause. In your case it will be longer, maybe minutes)Oh... and how to extract the audio? Suppose you use EAC, then there are several options. If you would like the track 'separate', then choose 'copy track 1 index-based' (which will give you track 1's gap
(which is the desired song) and track 1 itself). An alternative is creating an image of the entire CD... there is also the possibility to get the two first tracks merged (but i guess that's not what you want)
Hope this helps.