Putin's recent statements regarding nuclear weapons have once again threatened the global stability.

As a matter of fact, I would rather experience the world as it was during the ancient Ggreecek times.

In the first placeTo start off/Firstly, the foundations of most important hardajor sciences were layeid in the ancient Greece.

What do you mean by the most important hard sciences?

This particular example comes to show how important was science was for this magnificent civilizsation.

Furthermore, most people during ancient Greece times were focused on simpler jobs that were not nearly as stressful as today jobs today.

Hence, visiting this particular place andin time would be a stress reliever for someone who has to deal with the pressures of the current timesoday (today’s society).

Moreover, there is a rising nervousness regarding the environmental state of the world, whereas the nature didn't posed a threat during the old timesback then/during those days/back in ancient Greece.

As a matter of fact, the greeks respected nature at a levelto the point that some philosophers dedicated their life to studying it.

Having a good breath of the fresh air that the greeks enjoyed would have a positively impact on the body of someone who is used to feelbreathing the hideous/polluted air of a highly contaminapolluted cityies, such as Bogotá.

To conclude, ancient Greece poseis a great place for visiting during an hypothetical time travel situation.

“Poses” tends to mean something negative.

Not only was this civilizsation a knowledge based society, but it also hallowed a calm/relaxing lifestyle.

Additionally, they counted with a less polluted air compared to what we have right now, whichhad clean air as opposed to our pollution which will will enrich theour experiences there even further.

The world is currently facing a period of financial and health turmoil.

If you want, you can use the active voice by saying 'The world currently faces a period of...'. But this works.

Putin's recent statements regarding nuclear weapons have once again threatened the global stability.

Strongly motivated by the recent turn of events, I dare to state that these situations are indictments of our modern society.

In an informal setting, 'dare to state' would be strange to hear, and you'd be better off saying 'dare to say.' If you're making a speech or writing an essay, what you have works well.

As a matter of fact, I would rather experience the world as it was during the times of ancient Greece times.

In the first placeFirst of all, the foundations of most important hard sciences were layeid in the ancient Greece.

'Layed' is often used, even by native speakers, but it's technically an incorrect spelling.

This particular example comes to show how important was science was for this magnificent civilization.

Furthermore, most people during the times of ancient Greece times were focused on simpler jobs that were not nearly as stressful as today jobs.

Hence, visiting this particular place and time would be a stress relievef for someone who has to deal with the pressure of the current timesmodern period.

I changed the end to avoid excessive repetition of 'times'. Purely a stylistic suggestion.

Moreover, there is a rising nervousness regarding the environmental state of the world, whereas the nature didn't posed a threat during the old times.

As a matter of fact, gGreeks respected nature at such a level that some philosophers dedicated their life to studying it.

This should make it a bit clearer.

Having a good breath of the fresh air gthat the Greeks enjoyed would positively impact the body of someone who is used to feeling the hideous air of a highly contaminated city, such as Bogotá.

To conclude, ancient Greece poseswould be a great place forto visiting during an hypothetical time travel.

Additionally, they counted with a less polluted air compared to what we have right now, which will enrich the experience even further.

'Counted' is out of place here and I'm not quite sure what you mean.