Lame. The director is lying cuz why would a member of his crew be in a scene deliberately meant to imply it was a character in the movie?

Carpenter said he used a crew member to film the shadow scene. Deducing who it was based on the silhouette doesn't work.
My password is password

It wasn't Palmer. It was Norris.

Palmer
It was his shadow we saw when the Dog-Thing went into that room just before the screen faded to black (you could tell it was Palmer just based on the hair style as the shadow turned around as the Dog-Thing entered the room).

Go ahead.

Gay 4 Fugazi

Hey don, can u let me PM you real quick? I need to tell you a secret
you can block me again after its kl
(っ◔◡◔)っ Fugazi

It has to have been Norris! His hair matches the shadow of the person whose room the dog went alone.
Palmer and Childs shared a room so if Palmer was going to infect Childs, he had plenty of time to do it. But he doesn't. Why?

Gay 4 Fugazi

Greedo
(っ◔◡◔)っ Fugazi

This message has been deleted.

Although going by the filmmakers it was Palmer's shadow. Just looked more like Norris's outline to me.
After the Dog-Thing is taken into Outpost 31 by Clark, it would appear that its first victim is the man whose shadow we see on the wall of the room into which the Dog-Thing walks. This shadow wasn't actually from any of the cast members, because Carpenter wanted to leave the audience guessing who the shadow belonged to (the shadow was actually that of stuntman Dick Warlock). However, the producer, Stuart Cohen, explicitly states that it is supposed to be the shadow of Palmer.
THE SHADOW ON THE WALL was intended to be Palmer. At the time of filming David Clennon's silhouette was considered too distinct, a dead giveaway. Cinematographer Dean Cundey tried to soften the edges to diffuse the image, but in the end John used stunt coordinator Dick Warlock to throw everyone off the scent

• Cohen's blog, "The Original Fan".

Norris was clearly first. The shadow was pretty clearly Norris. Notice the hair shape and overall the shadow was too big to be Palmer. Palmer was a skinny dude, the shadow was that of a bigger guy (Norris).

Here is who I myself think assimilated who and the order it was done in in both the 2011 Prequel and the 1982 John Carpenter movie.
THE THING
(2011)
Griggs was Assimilated inside The Chopper by the Ice Block-Thing
The Dog was Assimilated inside it's kennel by the Ice Block-Thing
Juliette was Assimilated inside the shower room by the Griggs-Thing
Edvard was Assimilated inside of the Mess Hall by the Juliette-Thing
Sander was Assimilated by the Split/Face-Thing
Carter was Assimilated inside of the Spaceship by the Sander-Thing
John Carpenter's
THE THING
Palmer was Assimilated by the Dog-Thing when it entered his room while he was alone
Bennings was Assimilated by the Split/Face-Thing
Norris was Assimilated by the Palmer-Thing when the Lights went out
Blair was Assimilated by the Palmer-Thing while he was locked in the tool shed after it failed to get Fuchs

If we assume that the first assimilation that we see is the shadow on the wall that the Dog-Thing walks in on, it's Palmer.
The filmmakers said that the scene was originally filmed with David Clennon (Palmer) in the room, but then he was replaced with a stunt double because his silhouette was too obvious. If we knew it was Palmer from the shadow profile, the shock of reveal on the couch wouldn't be there.

I don't know if the shadow is Norris or Palmer, but regarding the OP's original question, "who was infected first," neither Norris or Palmer was the first one infected according to the film's co-producer Stuart Cohen.

One of these days I'm going to cut you into little pieces.

The shadowy figure that the dog takes over is Norris, you can tell since hes wearing a sweater.

There is absolutely no doubt that Palmer was taken over first.
Not according to the film's co-producer Stuart Cohen.

One of these days I'm going to cut you into little pieces.

There is absolutely no doubt that Palmer was taken over first. The first time the Dog is alone with anyone is in Palmer's room. Literally every minute before that the dog is in a room with multiple humans. You can speculate on the order following that (although I never understand what you'd want to, it makes no difference whatsoever what order they were assimilated after this) but Palmer was first.

Norris and then Palmer, Palmer's longjohns were shredded by The Thing.

The imitation versions always give themselves away by their suspicious behavior.
This!! So this. And it was an important part of the video game as well when your main playable character is in a group or with one other person.
WATCH - He touches the thing with the pencil eraser, and then he touched his lips as he was thinking about it.
He killed all the dogs, like a non-alien would. He destroyed the chopper and radio (he was going to use it for making his ship and it prevented people from leaving.) But this made him look like a crazy human, AND it forced him into isolation. LIKE the thing wanted. Remember, it could be part of a whole, and each piece will do what it has to to break off and survive, right?
That's what the isolation and crazy behavior was for: to break Blair-thing off, so it could work on its escape. While in the shed, he was digging a hole and putting together its ship.
Why would he infect himself though? Especially if he was already infected from doing the autopsy.
But I think IT realized that humans were too big or an adversary for it, so at some point it wanted to just lay low inauspiciously and rebuild it ship so that it could go home.
Fucking movie is BRILLIANT!

I don't care what other members here believe. Palmer was taken over first.
Understood, but on the other hand, some members may not care what you believe and insist Norris or Blair was taken over first. Just scroll up for examples.

One of these days I'm going to cut you into little pieces.

I don't care what other members here believe. Palmer was taken over first.

Palmer was taken over first. You see this when the dog walks into his room in the beginning.
But some members here have stated they believe the shadow in the room was Norris.
So you have conflicting theories.
Palmer says he ain't going with Windows, because everyone was suspecting Windows was an imitation.
Or.Palmer was human at that time and really was suspicious Windows was a Thing.
Norris was already the thing here. Norris got nervous and said, "Why me?".
OrNorris was human at that time and really was trying to avoid taking over leadership.
That's kind of the point of Carpenter's whole paranoia theme. A viewer's perception of behavior is not concrete evidence. Carpenter never gave obvious evidence pointing at any specific person all the way up till we actually see transformations.
As you state, Palmer took an accusatory stance. Does that mean he is an alien as you suggest? Childs also took an accusatory stance and he was definitely human at least all the way up to and through the blood tests. So an accusatory stance is by no means proof a person was an alien.

One of these days I'm going to cut you into little pieces.

Palmer was taken over first. You see this when the dog walks into his room in the beginning. Then Norris. Then Blair, not Blair first.
There are clues throughout the movie that can tell you when a character was transformed. Watch it again. The imitation versions always give themselves away by their suspicious behavior. Palmer says he ain't going with Windows, because everyone was suspecting Windows was an imitation. Palmer-thing blends in with others by agreeing with the suspicion and casting doubt on Windows.
What about Norris? Remember when Mac wanted someone to hold the keys. Norris was already the thing here. Norris got nervous and said, "Why me?". By shifting focus, blending in, that's how the thing always survived and slowly took over its areas.
Then Blair. I think Blair was taken over slowly starting with the autopsy. Watch it again. He clearly states that the organism appears to be dead, but the cells are still active. WATCH - He touches the thing with the pencil eraser, and then he touched his lips as he was thinking about it. It started transforming him then. So, remember what I said about the imitations casting doubt on others? Blair-thing comes out swinging, literally. He killed all the dogs, like a non-alien would. He destroyed the chopper and radio (he was going to use it for making his ship and it prevented people from leaving.) But this made him look like a crazy human, AND it forced him into isolation. LIKE the thing wanted. Remember, it could be part of a whole, and each piece will do what it has to to break off and survive, right?
That's what the isolation and crazy behavior was for: to break Blair-thing off, so it could work on its escape. While in the shed, he was digging a hole and putting together its ship.

If the thing can infect hosts on a cellular level anyone touching it could have been infected.
My theory is that both Blair and Fuchs were infected that way (probably during the autopsy). Fuchs burns himself, Blair loses the plot.
I'm also inclined to think the infections and assimilations are all random. Apart from Blair's escape ship there's little evidence of a plan or strategy from the creature.