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We live in Mexico so my experience is from there, but I've crossed the land border into the US at least 26 times in the past year and have never been asked for vaccination info for ourselves or our kids. From my experience you probably won't even be asked.
That said, while looking at the link you included in your question, follow that through to Frequently Asked Questions there is a section that explicitly says that children under 18 are exempt from vaccination requirements.
Entering the U.S. Through a Land Port of Entry or Ferry Terminal
Q. What are the requirements to enter the United States for children under the age of 18 who can't be vaccinated?
A:β―Children under 18 years of age are excepted from the vaccination requirement at land and ferry POEs.