Patience and persistence
Documents
Your driver's license (or government issued ID card)
Proof of address (utility bill, bank statement, insurance statement)
Copy of child's birth certificate
Proof of guardianship if your name isn't on the birth certificate
Copy of your child's Social Security Card
I've provided links to the three credit bureaus that will give you the detailed steps and forms you need to complete.
Do one freeze for one credit bureau and one child. Get a quick win, then continue through the rest.
Make an extra copy of the documents and save them in a folder with a date on it so you remember when you did this. (And if something goes sideways, you've got a backup.)
You are sending sensitive information through the USPS, so you want to make sure it arrives. You can decide whether you want to spend $10 for priority mail or just add one of the available tracking options. Personally, I would also make the trip to the post office.
Submit the freezes first, then go down all the rabbit holes that the provided links will take you down. It's easy to get distracted - get the important part done first.
There have been a number of health providers who have each had a data breach of sensitive information. It's one thing if T-Mobile gets hacked, but T-Mobile doesn't have your child's name, address, age, and social security number.
A preschooler has 10 years for something to go wrong with their social security number before needing it and will likely not find out until applying for credit (or maybe a job) for the first time. That's a long time for new types of crime to evolve.
The credit freeze is really the most effective tool we have right now.
Check out the links on the home page on freezing your own credit and locking your social security number. If you have children 18 or over, you can help them through that process.
I wouldn't spend money on active credit monitoring or LifeLock or any of the services that the 3 credit bureaus will try to sell you. You can take advantage of any free monitoring that the companies will offer when you get their "oops - something bad happened" letter, but the credit freeze is the best option.
Trans Union - Freeze Support Center | Credit Freeze FAQs
Equifax - MINOR SECURITY FREEZE REQUEST FORM
Experian - Child Identity Theft Services
USPS - Shipping Insurance and Delivery Services
NerdWallet - How to Prevent Child Identity Theft