As they obtained US citizenship by action of law when they physically resided with a US citizen parent in the US, yes, you can apply for a passport under the Child Citizenship Act.
It might be worth it waiting for USCIS to mail the citizenship certificates to apply if there’s no travel plans in the next year or so, because that would require less documentation.
The link I gave above lists out what is needed as secondary proof when applying for a passport under the Child Citizenship Act; I’ve reproduced below for ease. Anything below with “you” is referencing the person who will be granted a passport (your children):
Your foreign birth certificate listing your parent(s)
Evidence of your parent’s U.S. citizenship such as a U.S. birth certificate, Consular Report of Birth Abroad (CRBA), or naturalization certificate
Evidence of your permanent residence status. Examples include:
Permanent Resident Card/Green Card
Foreign passport with the original I-551 visa entry stamp
Your parents' marriage certificate (if your parents were married when you legally entered the U.S. and before your 18th birthday)
Documentation of legal custody when you entered the United States, if your parents were not married at that time. If your parents divorced after you entered the United States, provide documentation of legal custody at the time of your parent’s naturalization
Evidence that you resided in the United States in the legal and physical custody of your U.S. citizen parent. Your residence is the primary place in which you live. Entering the United States or temporarily visiting the country - even if on an immigrant visa - usually does not meet the requirement to reside in the United States. As such, legal permanent residence cards alone are not evidence of residing in the United States.
You need proof of residing in the United States with your U.S. citizen parent. Please provide at least two of these documents:
School or day care records
Utility bills
Employment records
Automobile registrations
Deeds or property rental leases
Medical records
Passport stamps
Evidence of your legitimation (if your parents were not married at the time of your birth). Legitimation means a father – whose child was born when he was not married – establishes a full legal relationship to his child. Establishing this relationship gives the father the same rights and obligations as if his child had been born while married to the child’s mother.
Examples of legitimation include:
Your parents' marriage certificate dated after your birth
Certified court order of legitimation
This link explains in more detail and this page contains the list I posted above. Note that any foreign documents not in English must have a professional translation with a notarized letter from the translator.
If you can wait to get a passport until USCIS automatically mails the citizenship certificate, it’ll probably be more straightforward. If you can’t, then yes, you still have the right to apply now.
If you choose to apply immediately, I would print out the two pages I linked above to bring with you in case the local worker hasn’t seen a case like this before. I also might apply immediately for a passport if you get nothing in the mail from USCIS within 90 days or if they mail you a green card instead.