Unfortunately, they realistically cannot. Basically every major infrastructure project gets loads of local opposition which would require substantial political will. However, the currently elected government is the government that let the rail infrastructure get that bad in the first place

AFAIK to fix reliability no new major infrastructure projects would be required (at least for most of the reliability offenses). They would just need to maintain/modernize existing infrastructure and rolling stock, so all things that aren't really opposable.

To achieve the Deutschlandtakt as noted in the article, yes new infrastructure projects are required, but I think most people would be happy with all the existing service running as well as it has ~15-20 years ago.