An ambiguity problem with "the first thing you remember"

To me, they are different. "What's the first thing you remember?" always means "what's your earliest memory?" never "what are you thinking right now?" This is so because present thought is not memory, again only in my view.

"what are you thinking right now?" is a question about meta-thought -- a thought about a present thought, just as "what's the first thing you remember?" is a question about meta-thought, but a thought this time about an earlier thought.

"A penny for your thoughts" is a lot different from "what's the first thing you remember?"

Normally, we do not refer to an immediate thought as remembering. For that, we would say something like "What's the first thing that comes to mind?" (as you already did yourself) or "What's the first thing that pops into your head?"

Also, "What's the first thing you remember?" often does not refer to the first memory in a person's life, but rather the first since some event, such as getting injured in an accident or being knocked on the head by an attacker.

Yes, it can take either meaning. So, you can say:

1. What's your earliest childhood memory?
2. What's the first thought/memory that comes to your mind?

Grammatically you are right, it could mean either of those things. However, the second would only make sense in a context where the memories would be limited in some way, because normally we remember things all the time.

So, the ambiguity is not a problem, because in any situation where it could have the second meaning, it would be clear what the meaning was.