My gf and I are visiting the embassy for a Schengen visa on Monday morning. We haven't bought her (or my) travel+medical insurance yet. Is there any company that has automated the insurance process and can send it to us by mail within, let's say, 24 hours?

We don't have time to wait for manual processing of this and need it QUICKLY. 

We've alway brought them online, you get an email almost at once and can print the certificate at home.

 

AXA is one company we've used, but there are many others https://direct.axa.co.th/TA/CoverageOptionPlan