Public schools may provide kindergarten readiness tests to screen children but I don't know if this is widespread, freely available, or if you have to request it in writing. I think some school districts use kindergarten readiness tests to screen children for special needs, LD, grade skipping, etc., but it varies by state or district.
In my state, except in two cities, late birthdays are redshirted and most districts are adamant on it regardless of the situation. Of course, I live in a anti-gifted state so there's also less chance of grade skipping or acceleration.
Public schools also offer other testing for special needs or 2e children (or use it to test for giftedness). Parents may request this under IDEA (federal act/law), but I believe you to request it in writing. Each state has special education laws and regulations that govern special education.
My state is anti-gifted and there are no gifted programs except at private schools. An eg/pg children might be assessed under special education if they suspect a child has ADHD, Asperger's, or etc. so they might get accommodated and services in the public schools but again this varies by district to district.
At a private school parents or the child may be interviewed or the child may spend the day at the program/school and see if it's a good fit. We had one-on-one interviews with the private schools before we placed my son in pre-k/k at the gifted private schools. We also had one-on-one interviews with public schools due to the 2e situation.
So yes, start vetting schools and teachers and what kindergarten entails in your area.
