Is it the Government Job to create Infrastructure?

Technically, you would have to define “enough”. But to get to what I would think is the heart of your question, as to how the market would provide these things at all:

The Privatization of Roads and Highways

Public goods

(see the links section in both of those as well)

How would a private road system work?

Making roads safer? How will privatization help?

"Free-Market Education"

“Disestablish Public Education”

“What If Public Schools Were Abolished?”

The Market for Teaching and Learning

“The Costs of Compulsory Education”

Peddlers of Ideas

“Why Home Schooling Thrives”

“Competition and Higher Education”

“The Common School Movement and Compulsory Education”

Education: Free and Compulsory

“Enterprising Education: Doing Away with the Public School System” (PDF)

How could a free market provide effective education for poor children?

Threads:

But…But…But Who Will Build All The Roads?

Subsidized Education and the Free Market

Question on the “Privatization of Roads”