It's unlikely that humans would go extinct anytime soon.
However it's estimated that there are at least 500,000 less births every year and including this year alone and more people are going and choosing to go child free.
Not everyone has or wants children so the population will slowly decline although we still have a lot of humans in the population.
So we are actually not on the verge of extinction at least in the next 500 years or so.
It may take another 1000 years before humans do completely go extinct but then again humans may never go extinct.
I personally believe that humans should go extinct because I'm so sick of how this world treats people and earth is not really a good place.
All we do is work and then die anyway and live at most 100 years or less before we do die.
The earth is running out of resources too and eventually we will run out of natural gas, gasoline, diesel etc and then it will be back to horse and buggy probably.