It was a nice little touch to connect them in the MCU. Maybe abit too cute but still a nice little touch

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In the MCU and widely in the comics these days, just about ever hero or villain is somehow related to trying to create weapons or super soldiers.
But no, the original Hulk origin was a more traditional accident. Along the lines of Flash getting hit by lightning, Spider-Man getting bit by a spider etc.
But yes, Nillindeiel's response is the complete answer for the MCU.
Reading my signature constitutes admission that I am correct. (Too late)

If you mean in the comics, the answer is no. He was testing a gamma bomb, when he spotted a teenager on the field. His assistant was actually a communist spy who didn't stop the countdown. The first Hulk movie had nothing to do with either the comic book or the second Hulk origin.
In the kingdom of the blind, you're the village idiot.

Just a correction on this:
Thor the line that a scientist (banner) was working on a super soldier serum and "went missing"
"Super Soldier" was never mentioned. Selvig's line was:
Erik Selvig: I knew this scientist, a pioneer in gamma radiation. SHIELD showed up, and that's the last I heard from him.
It's implied that Banner was attempting to replicate it for the army. That being said it's never implied Cap had any gamma radiation.
The thing to note in this regard is (and this goes to the OP as well) that when Banner's accident occurred he didn't know that what he was working on was an early stage attempt at reviving the super soldier program. Ross kept that from him. Banner had believed he was working on developing radiation resistance for the military.
Here's Ross' dialogue to Blonsky in TIH:
"We decided to dust it off, and give it another go, aiming to create the better soldier.
Banner's work was very early-phase. It wasn't even weapons application,
he thought he was working on radiation resistance
. I would never have told him what it was really for
, but he was so sure about what he was doing he tested it on himself. And something went very wrong or it went very right."
Nillindeiel
Agent Hill:
Then aliens invaded New York and were beaten back, by among others, a giant green monster, a costumed hero from the 40's. and a god.
Agent Ward:
I don't think Thor is technically a god.
Hill:
Wellyou haven't been near his arms.
~Agents of SHIELD; Season 1 Episode 1 "Pilot"

well here's the evidence where it is discussed during phase one
Thor
the line that a scientist (banner) was working on a super soldier serum and "went missing"
The incredible hulk
Tony Stark telling Ross "the super soldier serum was put on ice for a reason" this is obviously referencing cap
During the events of captain america pretty much anyone who was involved in the science between turning Rogers into captain america was killed off except Howard Stark. It's implied that Banner was attempting to replicate it for the army. That being said it's never implied Cap had any gamma radiation.

I wonder the same. Sad that we don't have a true HULK origins movie that's based on this universe. The Edward Norton movies was the start of this Hulk and that movie was set up for as a sequel to whatever happened to cause Bruce to Hulk out.

I hadn't heard it the first couple of times. I thought it was such a cool little connection between them all. Loved it. I almost wish we had seen Ruffalo do this storyline

I understand it was always
similar
research, but never directly connected. I thought it was a nice touch when they did connect it here.
Fabricati Diem, Pvnc !
RIP Terry Pratchett

I don't believe it was always the case. I'm pretty sure he was just experimenting with Gamma Radiation in the original story.