Well, the initial owner buys (or receives as a gift) the painting directly from Picasso. That's an easy one!
It gets more complicated later: experts assess the credibility of the painting by examining the ownership history, if available, the signature on the painting, the quality of the work, chemical properties of the pigments and canvas, etc. They sometimes get it wrong, though (cf. Beltracchi!). It's more a probability that a work is genuine, rather than a 100% certainty.
an original picasso is a historic artifact with the same paint that the artist himself used and his brush marks etc.
a copy isn’t. an nft is just bytes. a copy is exactly the same as the original. it’s impossible to get an exact copy of a picasso because he himself only ever painted one. you can carbon date it etc
There are experts that can verify Picasso. Digital assets are copied verbatim with 100% fidelity and zero error.