If someone has told Finn that he'd be meeting the Captain Cassian Andor, he would have taken them to the nearest med droid. But, there he is, on his way down to the meet the heroic captain. Finn's nervous and still a little sceptical, after all Captain Andor has been dead for roughly 34 years but he can't imagine why anyone would impersonate him here of all places.
When he reaches the buffet, it feels too noisy and full for what's about to happen but Finn supposes its a good a place as any. It takes him a few moments of scanning the room to locate the captain and when he does, Finn has to take several moments to really process the situation. It's him, it's really him. Finn would recognize that face anywhere, he'd spent enough time reading about the rogue one crew to know their faces.
It takes him a further 10 or so minutes to get his feet to actually move, because now that he knows this is legit it's almost harder to grasp. Finn has to stop himself from grabbing the captain's hand or worse, pulling him into a hug when he finally reaches the table. He stands by the table, staring down at Cassian in awe and not saying anything for an uncomfortably long time.
"S-sir, it's.... it's an honour to meet you, really, you're just one of my personal heroes." Finn said in a breathy tone, holding his hand out for Cassian when he'd finished speaking.