The only way to accomplish this at scale is to build something that is legit better and let the market decide. Anything else is just principled wishful thinking.
Start with a target small municipality in each country. Switch to SUSE (with a desktop that supports Active Directory), Collabora and what not. Then switch the mail stack. Then the files stack. Etc.
Next step is scaling it up to a small city, then a big city, then a province, and finally the whole country.
Parallel to this you do the universities and militaries.
The beauty of this is that the untold tens (hundreds?) of billions € in Microsoft / Google / Amazon support contracts will now instead flow into open source support contracts. Can you imagine the insane pace LibreOffice would improve at if a few billion € in support contracts was paid to Collabora each year?
One thing the government would have to resist is thinking that open source is 'free' and that they can cut their yearly spend on digital office stuff to the bone.
But that process is inevitable, it's already happening. What is not inevitable is hardware sovereignty. If EU doesn't have some form of hardware independence then they might just end up forced to use the US software stack.
Not necessarily. Red Hat is a billion dollar company just on FOSS support services and consulting. And if you put hundreds of thousands of clients on a completely novel FOSS stack, you're going to need several of those.