It is only possible to log into Google Account if on the JavaScript settings you enable "activate window". Perhaps it would be a good idea having that enabled by default.
This bug looks like: https://bugs.kde.org/show_bug.cgi?id=427133 But with a different root cause.
This sounds very strange, but I expect nothing less from Google. Thank you for your report.
You are welcome. May I ask why this isn't surprising coming from Google, just for my own information?
To login to Google you have to have to also have user agent with recent web browser version. On top of that I believ Google wishes to cage its users in its own products which Falkon is not part of.
My thoughts: https://youtu.be/c-lEw_FpSBo
Happened to me too, Workaround: send firefox browser ID. It's in Preferences, Other, Change Browser / Navigator ID. (translations vary) then select Mozilla/5.0 (X11; Linux x86_64; rv:57.0) Gecko/20100101 Firefox/57.0 either globally or for 'google.com' (Thanks to Franco https://bugs.kde.org/show_bug.cgi?id=416273#c1)