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The obvious answer is that people get older and (presumably, hopefully) retire from the workforce.

If your country's demographic is otherwise more or less stable, it means that by the time those 300,000 people age up to enter the work force, a similar number of people retire from the work force and hopefully live on their pension plan.

In addition to the other answers, it should be noted that jobs don't just exist independent of people. The only reason jobs exist is that people create the need for jobs, so more people means more jobs.

"300k people entered the labor pool" and "300k+ births a month" are very different things.

You can get to 300k new people in labor pool, if you have 150k people reaching employment age, and 150k of previously long-term unemployed people (excluded from the labor pool by labor statistics bureau) started looking for a job (because they decided such with low unemployment, they have chance to get the job even if they could not get it before).

And to get to 150k people reaching employment age you need more that 150k births, 20 years earlier.

We have no idea how many jobs will be available 20 years from now for people born now. It could be singularity and robots will do all the work. Or climate collapse could start WW3.

And then there is immigration, legal and illegal.

In addition to other answers. (+1 to Kloddant).

Note newborns will only enter the labor market after 20 years or more. The economy is supposed to grow (even when the population is stable) a lot in that time frame, so by the time anybody born today ends college the new jobs increase ratios is supposed to be a lot higher than today.
Of course, no one can give us a real number of new jobs created for 2039. But we hope it will be more than 300k.

"On average, 205,300 jobs need to be created every month just to keep up with population growth"

per Business Insider Aug 2016.

Their article appears to be an analysis of this issue, however I will leave it to the reader to debate the accuracy and/or validity of the conclusion. If the analysis was valid in 2016, I would think that it is equally valid 2.5 years later.

Quick answer. Money is produced by private and corporate bank loans. With a fixed base money supply (because bond rates have been flat for 40 years now) this means debt can not be repaid because it amounts to more money then there exists. So there things allow this to continue, new loans but this grows the interest leading to the other two. Alternatively the loans can default, or the banks can essentially give money back.

The give back is why we don't need 100% employment. Most middle class can live off investment and pensions. With enough principle it is trivial matter of funding.

This is in contrast to prior where you got the give back from a know, standard source, gov bonds. Reliable, riskless, standard insertion of new currency. Today bond rates have been flat and non competitive. With growing world economy private and corporate banks use debt to create new money and give interest back through literally any way you can think of. Insanely well paying do nothing jobs, artificial investment growth, or sometimes not at all, bankruptcy.

Other posters noted that you need to subtract the number of people who age out of the labor force from the number of people who reach the adulthood each year. In a thriving society, both numbers are substantially less then the number of births.

In a thriving society, a large fraction of the working age population does not work for monetary pay. They have better things to do: Homemaking, raising children well, gardening, volunteer work.

If a society manages to have 90 % of its working age men working, and 30 % of its working age women working, and does not have net immigration/emigration of working age adults, then the rate of creating net new jobs should average about 60 % of the rate of net new working age adults.