I upvoted Dutch and did not think anything else was needed; but in response to commentary I will add on.
This is an unqualified YES.
Amateurs spot new asteroids and comets all the time; it is just a matter of equipment that is affordable to many in the upper middle class, like Joe. Some people buy \$200,000 boats for their hobby, others could spend that on astronomy instead.
I have spent 40 years either earning in Joe's range or above it but working daily with people that earn in that range; and I know from personal contact it is plausible for some to spend lavishly on their hobbies. Perhaps \$70,000 a year would be an outlier, but not implausible. Make Joe a little older (warranting the higher remote salary) and he could easily have half a million dollars worth of equipment. He is technically minded, he can understand and compute the trajectories, speeds, etc. As a computer developer he can probably program accurate simulations to find places to look, or discover anomalies. Joe can be, effectively, the same as a professional astronomer with professional equipment matching the typical university observatory setup.
- Is it plausible that Joe will be the first one to spot it?
Another unqualified YES that apparently needs explanation. It is plausible that some amateur will find it. Why Joe out of the hundreds or thousands it might have been?
That is a question that does not have to be answered! In fiction, the author focuses on the characters that eventually get lucky or do something extraordinary; that is the nature of story telling. We generally do not take some random person and tell about their ordinary life where nothing of any real consequence happens.
Consider Stephen King's (SK) "The Stand". He focuses very early on Stu Redman, a reasonably intelligent guy hanging out at a gas station with his buddies in a small town in Texas. The Superflu, a bio-engineered disease that none of the characters have heard of, is about to escape and kill 99.999% of all humanity.
Why would SK focus on Stu? Because this gas station is about to be crashed into by patient zero, a soldier infected with the Superflu, and Arnette is about to be ground zero for the spread of this infection, and Stu is about to be the first person in the world to be proven immune; due to a 1 in 100,000 chance mutation in his DNA that has had no effect upon him so far.
What are the odds THIS gas station, out of millions in the world, is where patient zero dies at the wheel and crashes? What are the odds of THIS small town being where it happens, out of tens of thousands of such towns? What are the odds this guy is immune (1 in 100,000) and happens to be AT this gas station and hanging out with his buddies?
The odds of such a coincidence are beyond those of winning hundreds of millions of dollars in a lottery. But it is the fiction writer's prerogative and duty to focus precisely such situations because that is where the story is.
In SK case, each component is plausible, so suspension of disbelief is sustained. Somebody has to be the first survivor, so SK begins his story from the POV of that person, no matter how long the odds of any individual being that person. In Stu Redman's case, out of 7 billion people on Earth, the odds of him being both immune and the first are one in 7 billion.
I could say the same about Harry Potter: The odds of being the one out of billions is one out of billions. Or being the best secret agent, the President of the USA when extraterrestials visit or an asteroid strikes, or being invited to Jurassic Park, or being the best martial artist in the world, and so on.
Fiction writers are expected to focus on the one unique person that is going to be "The One" and tell their story.
So because it is plausible an amateur will be the first to spot it, of course it is possible Joe is "The One". Because this is fiction and the author would not focus their tale on anybody else but "The One." That is expected by the audience (readers, viewers, listeners) and does not break the suspension of disbelief in the slightest. On the first pages of a novel (or a chapter or other story cut that introduces a new character) we fully expect the focus to be on characters that will matter to the story line. The earlier in the book or movie these characters are introduced, the more important to the tale they should be (e.g. it breaks suspension of disbelief if the plot resolution comes from a character first introduced near the end of the tale; so much so we consider this to be poor storytelling [pejoratively called a deus ex machina]).
Somebody has to discover it and that might as well be amateur Joe; the OP has given plenty of reasons (perhaps too many) to tilt the odds in Joe's favor. Authors are nearly always telling the tales of people experiencing an extraordinarily unlikely string of individually entirely plausible and possible events or circumstances. Because that's where the story is!