First, it is highly plausible that worm holes can be established. If that is true, then it is simple to carry one end to your destination and to set it up to act as a transit system. The other problem is getting there and there it is a matter of using Dark Matter energy to continuously power the craft. Again, see below to understand that such a system can apply acceleration at any rate it wishes to establish a quick link up and bring a worm hole.
Curiously, i know how to do all this now though the worm hole work needs to be worked up with lab confirmation. In short, i expect success. The rest we have done or it has been done already elsewhere.
So yes, progressive technical evolution can allow us to access the whole galaxy over perhaps decades but not much longer. That is why local space is turning out to be crowded by curious aliens. I imagine we will be the same..
Space Travel Shorter Time Period than Thought