Technically I can probably do it in about 10 minutes because I've worked with these kind of stats before and know about packages that will get you this basically instantly (https://pypi.org/project/nfl-data-py/).

It's exactly 4 lines of code to find the correct answer, which is 2,227.

Assuming I didn't know about that package though I'd open a site like pro football reference up, middle click on each game to open the page in a new tab, click through the tabs, copy paste the rosters into sublime text, do some regex to get the names one per line, drop the new one per line list into sortmylist or a similar utility, dedupe it, and then paste it back into sublime text to get the line count.

That would probably take me about an hour.