You can sometimes get free formula through diaper banks and you can also get diapers as well for free if you meet the income requirements.
There's not too many diaper banks around as of now but you might have a diaper bank in your location or near you so you might check that out.
Some of those diaper banks just distribute diapers and I've volunteered at some that had formula and baby food as well.
You can also look at signing up for rewards for baby items and sometimes you can get free diapers that way as well and free formula.
As for formula though you can use WIC to buy formula for your baby but you cannot buy diapers with WIC.
Getting free diapers for a year can sometimes be possible if you sign up for Amazon mom or Huggies Rewards.
Some diaper companies even such as Pampers, Huggies etc have rewards programs where you can sometimes win free diapers for a year.
If you're struggling with money to get diapers then you can check out some free diaper banks that give you free diapers that are donated to them.
Using cloth diapers is also another option but requires work.
You can also try Pampers Rewards.
Other than that there's not much other ways to get free diapers and government assistance for diapers for your child usually doesn't kick in unless the child has a medical issue and is 4 years old or older.
Most times it's easier to just work and pay for the diapers for your child than it is to try and win rewards and free diapers for your baby.