Dutch government has explicitly funded quite some projects, e.g. libressl and libreoffice, but compared to budgets for closed source, it's still very little.

Here's a nice blog about how the UK deals with this.

https://governmenttechnology.blog.gov.uk/2016/12/15/next-ste...

As to infrastructure work, easiest way to help and still profit is to hire one or more developers that explicitly work on a set of FOSS libraries. That way you have that knowledge in-house and a connection into the community. Also, you'll have some highly motivated employees.