If you think about it really bluntly, survival of the species does not require every single baby born to survive.
So several factors at play, really. People had more babies in the past due to lack of contraception. But infant mortality was high. I think Hans Rosling actually has a good statistics video on this - as infant mortality goes down the number of children a family has goes down. The number of surviving children tends to stay roughly the same at around 2 per couple, interestingly enough.
So yes some babies died. They would have died from various things - more disease about before vaccination. Simple illnesses which we now treat would have been deadly, especially in babies. Childbirth was dangerous without modern knowledge and technology. Cot death, accidental suffocation from improper bedding. Accidents. Babies were often soothed with things which we now know are poisonous or drugs - alcohol, opium. There were dangerous substances around in the home. Smoke from cooking fires, lead in paint and toys, etc. In the past people didn't understand hygeine and infection so they didn't necessarily wash things properly or avoid contamination. Because there was so much death around, it was just sort of taken for granted. People didn't really think to properly investigate babies' deaths, they just assumed it was the way of the world and/or God's will.
There is an interesting website called the Baby Bottle Museum which has a lot of information on early bottles and pap feeders. We actually have evidence of people feeding babies on "pap" (which is basically mush, as others have said, made from things like flour, other animals' milk, any kind of semi-liquid food.) dating right back to Egyptian times, so it's always something which has happened. Whether it was as a supplement to BF or to replace BF, we can only really speculate, but certainly, humans have been feeding other foods to babies for a very long time.
Then the other evidence we can look at is the ways of less developed nations - there is lots of information about this in the book The Politics of Breastfeeding, which is a really interesting read if you're curious about this kind of thing. There are several nations around the world where breastfeeding still has a high prevalence and we can likely assume that practices here would reflect practices in our own society at less developed times. A recurring theme is that women would happily nurse each others' babies. Not only in a wet nursing sort of scenario, but aunties, even grandmothers, would help out a new mother who is not producing enough milk or who just needed a break. There is a different attitude - breastfeeding is something which happens, it isn't a complicated process to get right. And supplements are given almost everywhere except in those nations where food is scarce.
I do think that we have lost some of our sense of breastfeeding awareness in that most women by the time they come to give birth have never even seen anybody else breastfeed before. In past times when women had more babies and the spheres of the sexes were more split, young women would have been around more breastfeeding mothers and had chance to witness and learn first hand. They probably learned some old wives' tales, too. But they wouldn't have had the anxieties that we have about babies feeding for "too long" or wanting to see how much the baby had taken because they wouldn't have had that option. Now if we want help with breastfeeding we often have to seek it out and the experts we turn to, really, are experts who have just observed a lot of breastfeeding. Some of our modern knowledge of BF comes from science, but a lot of it is still observation. It stands to reason that if you'd always seen breastfeeding happening around you, you'd pick up knowledge that just isn't as common today. This is also backed up by the stats we have which show women are more likely to breastfeed and to succeed at breastfeeding when their family and friends have breastfed.
It's a complex topic. It's certainly not as clear cut as to say "Everyone could do it in the past!" but I think it's also simplistic to assume that babies were starving to death left right and centre because women couldn't breastfeed. The evidence we have of BF-dominant nations/cultures suggests that this wouldn't have been the case. I do believe that failure of BF must have contributed to infant mortality, but not as highly as is being suggested here.