A classic way to bridge the gap is to put a great academic brand on your CV. For example, you could work as a research assistant in CS for a famous university (e.g. Cambridge, Imperial, ETH).

Since the salaries they offer are low, the competition won't be so intense, and they will offer support to relocate. Once you have a foot in the ground, you can apply to great industry jobs.

A more elaborate plan would be to obtain a PhD at one of those institutions, but that is quite time-consuming and the benefits might not offset the costs.