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It would seem that most people who are born will eventually enter the workforce. Maybe that entry is delayed due to college or enlistment or that very important backpacking trip through Europe, but it seems that most people born will eventually get hired somewhere.

So when you hear that the economy added less than 200k jobs, but over 300k people entered the labor pool, that we've really got 100k more unemployed people? It doesn't seem like anything less than 300k job is even breaking even against population growth. What am I missing here?

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 answer above, it should also be noted that jobs aren't just something that exist independent of people. The only reason that 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.