No, they can’t - not in anything resembling a reasonable timeframe. The only benefit they gain is the ability to have their child sponsor them once they are adults. It takes 18 years to become an adult, 1 year to petition for a green card and 5 years to get citizenship for a bare minimum of 24 years. I said 27 because I used 21 years of age to calculate. That’s not a benefit really, taking into account the fact the children have to pay taxes for that whole period while living abroad. Then the child has to want to live in the US, move there and sponsor their parents at their sole discretion.

The idea parents get massive benefits for having a child in the US is an “anchor baby” in colloquial terms, pejorative or not. It applies colloquially to legal and illegal immigrants - and so does the family reunification visa process. The idea of an anchor baby is a myth.

Your single anecdote is not outweighed by facts, it’s not precedent unless it happened in court (the whole immigration process is almost entirely discretionary and capricious, you can be denied or delayed for any reason, and you have almost zero recourse because you as a foreigner have no right to immigrate to the US except by asylum — and no amount of “my parents got in” is going to change the mind of a consular officer or immigration judge). You didn’t read the article I sent you, you bragged about it, and you’re still wrong.