Is it possible to figure out what keywords are driving a traffic to a particular page? Our's for instance is a PDF file that is not being tracked by GA.
In Google Search Console, click on Search Analytics, then select Pages. You can use an include only filter for
You can also track PDFs in Google Analytics.
Here you can find 2 complete answers about tracking PDFs in Google Analytics: Tracking PDFs properly on our website
So, you can use Events or Virtual Pageviews. Your choice.
Remember that keyword data for analytics is very limited and you'll have only a small spectrum of them. But it can be interesting because now you can see the path your segmented audience can take before reaching a PDF, even when PDFs are not "landing pages".
This is not possible using Google Analytics, unless you implement a server side proxy script, that sends a request to Google Analytics before sending the PDF file to the browser. See https://developers.google.com/analytics/devguides/collection/protocol/v1/
I would suggest that you use Google Webmaster Tools, which allows you to see search requests from Google (but not other search engines unfortunately) for certain pages, so you would be able to see which keywords were used before downloading your file. This is visible under "Search traffic" -> Search requests and then clicking the "Popular pages" tab.