Infrastructure projects provide jobs and income for the workers (well-being growth). They enable economic activity providing jobs and income more widely (well-being growth). The cost of creating the money to pay for it is... nothing.
Nothing, as long as people understand that nobody lost out. People will talk about inflation and devaluation at this point, but this happens because confidence is lost. And that's all.
I've yet to find someone who can explain to me why this isn't so. The devaluation thing only happens because those who hoard wealth in a particular currency fear that they'll not be able to exchange it as beneficially in another currency.
But there should be no need to. If money was understood.