Ford's first official factory built crew was in 1965... but this is kind of a trick question. Why? Because there were Ford crew cab trucks built BEFORE 1965. Here's the scoop... and all of the following is to the best of my knowledge and recollection.
Before 1965, Ford farmed out trucks to a number of coachworks across the country to convert the regular cab trucks to crew cab trucks. These trucks were sold at the Ford dealerships (or even directly through Ford for large orders of vehicles) and many of them still carried a Ford warranty since they were authorized builds. Were there trucks that DIDN'T carry a Ford warranty? Yes... but that certainly wouldn't matter now. Anyway, to the best of my recollection, most of them were 4 door trucks with standard features... BUT anyone could order a truck the way they wanted it to be thus there were trucks that had only 3 doors (usually, the passenger side was the side that had the door deleted) or even only 2 doors (but still with a 4 door type cab). Finding one of those 2 or 3 door trucks would be super hard... but they do exist. I saw a 3 door truck for sale up in Alaska less than 2 years ago, for example.
So what's the earliest that Ford crews were built by an outside coachworks...? That's arguable. Most people will say 1957 or 1959 but I know that some funky trucks were built way back in the 1930s and yes they could be called Crew Cab trucks in spite of the fact they weren't factory authorized nor were they called a "Crew Cab" truck. Essentially, what they really were... could be called customized trucks that carried more than 2-3 people. Ironically, I don't think anyone even used the term customized back then... and hot rodding as we know it didn't start until the 1950s though that too is arguable. Sticking to reality, I'll say that trucks that were actually called "Crew Cab" trucks came about in the 1950s but I wouldn't argue over it... there is no real actual answer as far as I'm concerned.
In reality, anyone could order a truck or group of trucks as they wanted them to be back then. As long as the orderee specified exactly what they wanted, had acceptable schematics and agreed to a price, the trucks were built to buyer specs. A buyer could even get any color paint they wished or type of paint... as long as they were willing to pay for it. As you might imagine, this made for some interesting trucks, especially those built for city, county, state or government entities like fire departments or public utilities.
The bottom line though is that there were plenty of crew cab trucks of various designs built... and finding one shouldn't be too tough. I've seen many pictures of trucks that were Air Force maintenance trucks... or were bought and used by a logging company, railroads... outfits like that. I also used to drive them at work every single day... when I worked for an airline. All the crews at the airline were identical based on the year of the truck because the airline bought them in large numbers in one model year... and kept on using them year after year. The oldest ones were from 1973.
As for Ford factory built trucks... Ford finally decided to start making these trucks themselves and cut out the middle-man. Almost. I'll get to "almost" in a sec though - first things first. The year was 1965 and the same rules as before applied... more or less. According to what I've read, you could order these trucks as you wanted them... as long as you were willing to shell out for what you wanted. For the really weird designs, Ford did stick to using an outside vendor unless the number of trucks ordered was a large number. For the standard versions Ford was already building with their own base design? All were built in house though you could order them with a few changes such as with an engine choice, trans choice, paint colors and interior trims. In other words... things that were easy for Ford to change on the assembly lines. However, the same basic design of the trucks was the same.
So, from 1965 onward, most of the crew cab type trucks that you'll find will be 100% factory built by Ford and they'll mostly look the same as any other Ford crew for each year. In other words... they'll have 4 doors, have standard drivetrains and use regular Ford colors. From the back of the drivers seat forward to the front bumper? They'll match any regular Ford truck using all the same parts. Usually, the beds also were full sized beds and I'll elaborate on that. Short, wide boxes were normal but there are a few full-length box trucks out there too. Those trucks are REALLY long! A few years ago, I saw a 70s 4x4 crew that had a long bed on it. Fully restored and it was beautiful. However, I doubt I'd want to ever attept to parallel park it. It was like a limo in length! Wow!
Hope all that helps... and was informative. I personally like the crew cab trucks, especially the factory 4x4 models from the late 60s and into the 1970s. Finding one of those is also tough... but they're out there. It will be easier finding a crew from the 1980s... but if you do a nationwide search, there are plenty of trucks to look at. My best advice is to have patience... and pass over any truck you won't truly be happy with. Note that a lot of interior parts for crews can be tough to find or even impossible to find... but all the regular stuff is as available as it is for the standard models. Best wishes!