Breaking into US from Bocconi

So, I’m Central European and starting a bachelor in economics and finance at bocconi (Milan) after the summer. So far, I’ve been a Sumer intern at a vc firm and am going to do an internship in the PE department of a law firm this summer. My goal is to get into IB (eventually probably pe/hf) in the US, but unfortunately my ivy day went badly. I know that bocconi is a target in Europe, but I don’t really want to get stuck in eu. Hence, I’m wondering about what my best option would be.

1. Transfer: assuming I do well in my IB exams, should I do my best to transfer to an ivy after first year?

2. Bocconi -> London -> NY: I’m also considering just grinding at bocconi, doing the cfa lvl 1, internships etc. How realistic would be transitioning from a full time role in London (assuming I get an offer after bocconi) to a US firm? Either from IB to IB or from an IB to a PE/HF role.

3. Assuming that the transition from London to USA is realistic and given that I aim to end up at a HF or PE firm in the US, would it be better to go into IB first or try to start with a Hedge fund / pe firm from the very beginning?