No need for absolute pitch. All you need is relative pitch. You play a note, compare to the note you heard, maybe even play them at the same time. And then change the note till you find the right one.

I thought the same for a long time and it really discouraged me. My natural pitch recognition is pretty bad. What helped was starting with very simple melodies and songs, so I could get familiar with the most common movements. That made it easier to figure out progressions, because I learned how to narrow down the options. I’m still not great at it, but I keep improving. That’s why I think it’s trainable.