Depending on the scale you use of course, SpaceX recently overtook Blue Origin, which is a strange statement. SpaceX overtook Blue Origin several years ago. The new Glenn was never assembled once and the BE-4 rocket engine never did more than run on a test stand, it was only one engine at a time, and we all know that if you use too many engines, a lot of things can go wrong. Vibration for additional components that don’t want to cooperate the chance of a problem is X times greater with X number of additional machines. (One of the reasons I think about SpaceX is that they launch 33 things at once, which is actually a bit harder than 3 engines or something)

Blue Origin should have a lot of exciting things on the drawing board anyway, and they’ll have a nice rocket when they finally get New Glenn up and running, but they won’t be on par with SpaceX until SpaceX decides tomorrow is Starship and Super. Given the speed at which the heavy, Blue Origin rockets are building, New Glenn has little chance of reaching space before SpaceX.

As for a launch site outside of the US, I imagine they’d have to be a little further south or somewhere in the Pacific Ocean to get the logistics needed to get the missiles working there. Because it would involve less bureaucracy than the US.
As far as production potential is concerned, there is actually a large group of people who have worked, are still working, and can work on rocket projects in Europe, which is very underutilized compared to the American market. A fraction of those with the necessary knowledge work for one of the major companies like SpaceX, Boeing, Rocketdyne, and Blue Origin, or for one of the many smaller startups. That said, if you’re looking for talent, it’s definitely not a bad idea to fish outside that pond.
Acquisitions are definitely not a bad idea as it is much less complicated than setting up a company yourself and attracting people, with the added bonus that if you take over the right companies you can also get your hands on useful technology.