This varies wildly, based on your chosen lifestyle and whether you have only one or multiple kids.
If you are using paid childcare, that expense is going to be massive. If a parent or other family member is caring for them, no cost.
If you have one child, you are paying for the bassinet, crib, car seat, booster seat, clothing for every age, and getting one child’s use out of them. These costs don’t change dramatically for two or three preschoolers, one after another, vs. just one.
For clothes, you will need most of another wardrobe for two genders (excepting some of the more expensive items, like snow coats, snow bibs, and shoes, which can often be gender-neutral for little kids). Little kid clothes in great condition are easy to find at thrift stores, because kids at that age grow out of their clothes before wearing them out. Often mom friends will pass hand-me-downs back and forth to each other for a lot of savings. Up through about the age of five or six, I budgeted $10/month times the number of kids for their clothes. It would have to be more with only one kid, though. After that, they grow more slowly, wear out their clothes more before passing them down to the next kid, and good thrift store finds are therefore harder to come by.
If you cook at home, you can easily feed a preschooler on $100 per month without stretching at all, less by exercising some minimal frugality.
Preschool is expensive. Preschool activities at home are extremely cheap. When I was homeschooling at the preschool/Kindergarten/1st grade level I budgeted $10/month for all four. Lessons are expensive. I acquired their fractional size violins from shopgoodwill.com for about $60-$70 per violin size (roughly 6 months to a year per size at that age), they passed hand-me-down violins down like clothes, and that was the cost of their music lessons. I taught my preschoolers violin, and also a friend’s preschoolers in a barter for some lessons in my friend’s expertise for my older daughter.
Disposable diapers are expensive. The cheapest kind from the cheapest source was about $30/month, more when they are an infant and go through more diapers, or if they are big for their age and need the upper sizes before potty training because the larger ones are more expensive. Pull-ups are a waste of money. Unless you fasten them too tightly, potty trainers can pull a disposable diaper up and down just as easily as a pull-up, and they are way less expensive. High-quality, easy-to-use modern cloth diapers are spendy, but still a great savings over disposable. Cloth diapers used for subsequent children are a massive savings over disposable.
So when we had four kids ages 1.5, 3, almost 5, and 6, we were spending about $200/month/child. We were lucky in that the family plan rate at my husband’s government job was only $100 more per month, so $25 more per kid. We used some cloth diapers at home, but disposable about 2/3 of the time. We ate food cooked at home, but were not extreme in our food frugality. Utilities are really only a small difference. Their little clothes at that age don’t take nearly as many loads to wash a full wardrobe as when they are older, and giving a little one a bubble bath in the kitchen sink really doesn’t use all that much hot water.
I found it very easy to spend dramatically less than average estimates for child rearing.
ETA: It probably helped keep costs down that we lived in the back end of beyond. There were no expensive family activities to forgo. There was no zoo, no pool, etc. There was story time at the public library (free), and there was the great outdoors. So we went swimming in the mountain streams and the lagoons at the beaches and we went hiking and clam digging and beach combing and blackberry picking in the woods and we got together with friends at the park and we went to the library. A Christmas tree cost $5 for a permit to cut one yourself from public land. There was nothing to spend money on. There wasn’t even a drive-through restaurant or a movie theater in our little town.