I am not personally old enough to remember a time before infant and baby formula were commercially available. And I think all the specialty formulas on the market now for various allergies are even newer still.
But there have always been some women who for whatever reason can't breastfeed. For one, sometimes you just don't make enough milk. I know wet nursing was done and was probably the logical second choice, but what if for some reason that was not available to someone? I'd imagine low income mothers could not afford to pay a wet nurse. And maybe in a small rural environment a wet nurse was just not available. So what did mother's do?
Adjacent to that, were nondairy recipes for formula ever used?
The first commercially available baby formula was made in 1867, so, I'm pretty sure nobody alive is old enough to to remember a time before formula.
In the past, is was very common for people to live with or near their extended family, and it was pretty normal for more than one woman in an extended family to have a baby who was still nursing at the same time, and so able to feed a relatives' child along side their own. various writings from ancient Egypt and Greece mention wet nursing and cross nursing, and myths around the world mention milk brothers, or other terms that meant two children who were not siblings, but nursed by the same woman because the mother of one of them could not feed her child. (for any number of reasons)
When this was not possible, animal milk was used. a sort of baby bottle made from a cow horn was used fairly widely in Europe in the middle ages. And clay bottles with a nipple shaped spout have been found in the graves of infants https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1988630/?page=5
If even animal milk was not available, babies would be fed some kind of gruel. From a spoon, cup, or one of the baby bottles I mentioned. But, even the earliest records of this recognize that babies fed this way were much more likely to be sickly, underweight, or even die, than babies fed some kind of milk.
/u/amifufu has previously answered Before we had things like Formula, how did infants whose mother died in childbirth get the necessary nutrients that are in breastmilk?
/u/mimicofmodes has previously answered In older days let's say before infant formula was invented how did lower class/poor families tend to/feed newborns in circumstances where the birth mother died during labor and couldn't afford/ get a wet nurse.
/u/Superplaner has previously answered Before specially made baby food. How did the people of your era feed their babies?
More answers remain to be written on this topic.