Does recycling lead to fewer jobs? Say I buy a glass bottle, I can either put it in the landfill or recycle it.
My understanding is, glass will breakdown into sand. (Not sure how well though, since we sometimes find glass from Roman times.) Alternatively we can recycle it.

But I was wondering wouldn't this put some people out of work? Such as the people who have to mine all the silica for use in making the glass in the first place. And considering it is more economic to recycle glass, this seems like fewer humans would be needed.

Therefore could I make the case that not recycling my glass bottle is helping with employment. On the other hand, recycling might be helping the economy as a whole and there might be more money in the economy for public sector jobs. Which is right?
Any invention that replaces human labor puts an end to that specific task. Glass recycling eliminates (or decrease) the need for silica-gathering task. Typewriter eliminates the need for printing press typesetter. Etc.

Those people whose tasks are eliminated will get reallocated to their most productive use. This might be in the form of job change (silica miner move to coal miner), or might be in the form of task redefinition (the book Prediction Machines describe how self-driving school bus might shift the main task of a school bus driver to an adult who oversees and "teaches" the schoolchildren.)

Going back to your question, recycling also creates new jobs. They need people to sort bottles, maybe drive a recycling truck, etc. So whether an invention leads to more or less job is ambiguous.

Added: While the effect on a specific industry might be quantifiable, if you take into account job mobility, etc. then the effect on the whole labor market is ambiguous.

Regardless, an invention that increases productivity should increase the size of the pie. We can produce more from the same resources. How that bigger pie is divided, however, is another very important question altogether.