Here are two versions of the sentence "Michael once said he wanted to be a musician": --> "This one time, Michael said he wanted to be a musician" (something that happened once in the past) --> "In the past, Michael said he wanted to be a musician" (something that used to be true, but seemingly isn't, any longer) The "Michael once said..." construction is very elegant and you're more likely to see it in written English, or during an inspirational speech. You can certainly use it in casual conversation (I sometimes do!) but you're probably more likely to hear people using the other versions. (really hoping this response goes through this time, as I'm not sure what about my previous answer upset the filters. hope it's helpful!)

"once" means one time, and in this example the inferred meaning is one time "in the past," because the verb "said" is in the past tense.

"Once" does not change the meaning of the sentence much. All it does is add a bit of specificity, similar to saying "I remember him saying".

once = one day

one time