(edit: corrected below)
Less handwaving, more cites[1].
[1] https://www.cdc.gov/nchs/nsfg/key_statistics/b.htm#agefb
https://www.pewresearch.org/fact-tank/2015/01/15/for-most-hi....
Similar breakdown in red states vs blue states. Blue states have much older age of first child, on average (because of correlation with educational attainment).
In fact the gap we should talk about is the gap between college-educated women and the rest (which stands at ~8 years)
the original cdc numbers cited are perhaps not best way to look at the matter, because they include women who were giving birth in 80s and 90s.