Slowly and with a lot of patience.

> 640 light years away

Inventing a better telescope would be quicker. Granted we would only see how they looked like ~640 years ago, but that's not a long time for measuring their technology level, especially if their average lifespan is similar to ours.

> but that's not a long time for measuring their technology level, especially if their average lifespan is similar to ours.

2022-640=1382

The age of tech. advances such as water mills and three-crop rotation.

This is just about the time banking became a thing in Italy. Most(?) humans would still be in pre-history. Maybe you could detect increased activity along the silk-road if you look closely.

Pollution levels in the atmosphere would still be dominated by volcanic activity. No guarantee that this planet would ever get anywhere...

> Most(?) humans would still be in pre-history

This is a very non-standard use of the term 'pre-history'.

Or if "they" are a thousand years ahead of us technologically then 640 years ago could be when they started building space elevators and large orbital structures.

Sure, those don't feel much like tech at our current pace of change, but it's millions of years further up the tech tree than, say, feathers, thermoregulation, photosynthesis, or multicellular organisms.

> 640 light years away Hmmm, how are we going to do this?

By using the sun as a giant lens:

https://www.youtube.com/watch?v=4d0EGIt1SPc