Yhe sink drain tailpiece is threaded. It is longer than necessary. If you feel handy you might cut it as short as possible (I'm assuming you know what to do with threads once cut).
Then, with a short sink drain tailpiece, it looks to me that you have enough height to continue with a "normal" installation.
Code requires the P trap "weir" to be at the height of your drain pipe. So you are correct in thinking that you only have two options. One is to open the wall and rebuild the drain pipe at a lower height. The other option is to get the P trap positioned at that right height, much higher than that tailpiece will allow right now.