Population growth was caused by progress in the form of industrialisation, not vice versa.
Yes, I agree, it was enabled by industrialisation that made food plentiful and advances in our understanding of microbiology that dramatically cut infant mortality.
But, it still required the will of individuals to reproduce in numbers - nobody held a gun to anyone's head and told to them to make babies - for populations and economies to grow and living standards to advance as far as they did.
I can't prove this, of course, but gut feeling is that if people are optimistic about the future and strongly believe that that tomorrow will be more prosperous than today they are more willing to reproduce and pass that opportunity onto the next generation.
But during the period you are talking about reproducing was not really something most people chose to do or not do, it was just the consequence of sex. Married women had babies until they were too unhealthy to do so. If the mothers and babies were well nourished the population increased fast, if they were badly nourished or otherwise unhealthy more died and population increase was slow. The only role optimism played was when someone said, 'oh shit, I'm pregnant again, hope we can afford to feed this one.'
Plus societies had social norms to limit growth - young men and women who had little access to family resources (a farm or a trade) because of birth position went in monasteries and nunneries. Even in wealthy families - the first son inherited, the second son went into the military, the third son went into the church. People didn't marry young (young marriage is for pioneer communities), they got married when he had a trade or farm and she had a dowry and savings. I totally forget where I read it, but young women not of the wealthy classes didn't marry until their mid to late 20s, and men until often their thirties (or forties).
And of course the odd epidemic reduced family size, as did the every so often famine. Rh incompatibility had an effect.
Basically we have gone from having lots of babies but with few making it to adulthood, to having lots of babies and most making it to adulthood, to having just a few babies almost all of whom make it to adulthood. Our social norms haven't fully adjusted to the change in infant/child mortality.
It also depends on the culture.
You're right, in British culture, for example, many working class woman didn't get married until later because they weren't allowed to work many jobs if married, so unless they could find a spouse who could support them leaving the workforce, they would just stay single.
Men who worked service on estates also couldn't marry unless they were willing to leave their jobs because they lived on the estates and couldn't have dependents living with them in servant's quarters.
I'm sure they impregnated many women, but they weren't often getting married young and having a ton of kids because of "optimism."
Economic optimism is more of a product of class mobility (perceived or mythical) and is a fairly recent concept in most modern societies, so the optimism from that is a very, very brief anthropological phenomenon.
It tracks though with a particularly American bias to perceive the post WWII era of the 50s as some "norm" that the world is constantly deviating from.
But even then, when I've spoken to people who had kids in the 50s, it wasn't out of a sense of optimism. The most common reason for wanting multiple children was out of worry about child death.
My grandmother, who NEVER would have had children had she been born later, had 4 daughters and was, well, a terrible parent, but she was horrified when my mother and aunt only had one child each and would frequently say, I front of my cousin and I when we were young "but what if she dies!???"
I've heard this from many mothers of that era. It was a very normal thing for them to worry about because their mothers instilled this in them.
Remember who that generation was raised by. I think it's pretty reasonable to say that the parents of that era weren't as "optimistic" as the boomer children they produced who retroactively view that era with rather intense rose-coloured glasses.
However, they're the very generation that started having less kids because they started having more freedom and choice. They're also the first generation to really start romanticizing having children because it *was* a choice.
When having kids isn't much of a choice, it's not romanticized as much. The many senior ladies I've spoken to have always been rather pragmatic and generally negative about the experience of motherhood. It has generally been viewed by folks I've spoken to who gave birth before 1960 as more of a chore than a calling. Especially when they talk about having daughters.
In my experience, it's more their children who equate having children with life purpose and meaning.
It's the same way marriage has only become a romantic thing amplified to incredible meaning and purpose since people started having the option to choose it.
Marriage actually had to be actively branded and marketed by the government as a romantic thing, and this campaign has its roots in white supremacy.
White married couples were so miserable, hated each other so much, and were so disgusted by one another that the government felt an urgent need to step in and convince white folks that marriage wasn't the worst thing in the world to protect the institution from being taken over by all the black folks who were starting to get married.
No joke, this is where douching comes from, because men were so grossed out by women after the puritanical nonsense of the Victorian era pitted the genders so firmly against one another. So a major effort was made to get women to be less gross and more palatable to the men who hated them and kept beating them and killing them. Which was becoming a major problem.
Much of the 50s notion of marriage, gender roles, and procreation in America comes from white supremacy/eugenics propaganda from earlier that century.
Historically marriage and having kids has never been about hope and optimism, it's been about obligation and desperation.
Paradoxically, it's the option to choose marriage and children that has elevated it to this great, meaningful, aspirational thing. But that has also lead to their decline.