Man I struggle with this so much.
What I try to do is just not offer any suggestions or feedback out of the gate. Just let them talk, nod along and say things like "man, that must suck" or "sorry to hear you're dealing with that".
Once they're done, I try to say something like, "you know, when I was going through something similar, here's how I felt". I think that lets them feel heard, and clearly signals that your intention is to relate to them rather than one-up them.