An existence proof is very different from a constructive proof!

Quite so. However, it does give reason to hope.

The question is, will this take decades or centuries?

If you look at Moore's Law coming to a close in silicon around 2020, and we're still so far away from a human brain equivalent computer, it's easy to get disheartened. I think it's important to remember that it's at least possible, and if nature could happen upon it..