Science fiction set on generation ships tends to be extremely gloomy for good reason.
It's particularly interesting I think because now that you've brought it up, it seems to me there is a similar issue with much Earthly colonization or frontier expansion, and I've never seen it mentioned.
For example, anyone who left England to start or join a New World colony early on, when settlements were far apart and it was a struggle for each to survive, was entering an environment where their children would have a much harder, much more constrained life than they could have had back in England.
Were there debates back then about the morality of moving somewhere where you descendants, possibly for generations, would have harder lives than if you stayed where you are?
Of course I'm also assuming that the majority of the colonists were not only dirt poor, but also ignorant and uneducated and shamelessly lied to by the promoters of colonization.
In outer space, cosmic rays will make this process faster. Also, in outer space, it will need a constant source of light for biological reactions, and also just to keep from slowly cooling down to 0k through heat emission.
A more human-sized comparison is "100 average single-family homes in the US, all filled to the brim with rice". Or 60 ISSes, all filled completely with rice. Per person. And this is volume, not taking into account the weight of rice.
Minimum sustainable population size seems to be about 100 people, so consider how large a ship you'd need just to fit all that rice storage.
On the other hand, it is under two Mount Palomar observatory domes full.
I'm assuming anyone building a generation ship is going to build it in space, not build it on a planet's surface and then try to launch it, so size is not really going to be an issue.
The big engineering issue will be propulsion. We don't have anything now that could drive such a ship. My guess is that this is either something we'll have within the next couple hundred years or we'll never have it.
I'm assuming that by the time you want to build this kind of ship, you've gotten raising people from frozen embryos or frozen eggs and sperm perfected, and that is where most replacement crew would come from. That should greatly reduce the crew size needed.
I think we'll be able to handle the biological side of this within a hundred years, with a good chance of it being quite a bit sooner than that.
Keeping a computer running in outer space for a few thousand or hundred thousand years is a gigantic engineering task, far beyond anything we could achieve today.
And of course, in reality its unlikely you could rely on a single computer system and on 0 propulsion. It's far more likely that you'll need life support, engines, complex medical equipment, cooling systems, lights, all sorts of mechanical parts that will need power, replacements, and that degrade in time, especially at such huge scales.
For a generation ship, are you referring to all the machinery that can maintain a balanced ecosystem of plants and animals and humans in order to provide food for the people during the trip to the new planet, and to make all the things needed to keep those people healthy during the trip such as medicine and drugs?
If so, there may be a way around that. Send all your colonists as frozen embryos or frozen sperm and eggs. Your ship only needs life support then to keep alive the people who run the ship. For food, don't grow it. Take it with you.
At first taking your food with you seems absurd, but if you had a food with the same caloric density as rice, enough of it to provide 2000 calories/day to one human for 100k years would fit in a sphere with a radius of 24.4 meters. So once your technological civilization figures out a way to preserve food such that they can make a rice ball equivalent with a 100k year storage life, a generation ship with a small crew becomes a whole lot more feasible.
For replacement crew throughout the journey, you can do a mix of using whatever kids the crew produces the old fashioned way and using kids produced from some of the frozen embryos/eggs/sperm.
I think technological civilizations will reach the point of being able to do this well before they are millions of years old. We aren't too far from being able to do it ourselves. We are probably farther out on the propulsion for the ship itself.