Should I even look at it if I'd like to land on SWE position eventually? I remember that internal transition from SRE to SWE is hard. A transfer from UX intuitively seems even harder... The reason I'm recommended a UX role after failing an SWE interview is because while I'm a full stack dev, my expertise is inclined towards front end a bit. (Did a lot of ASP.NET/GWT/Angular.js/Angular/React development)...
Hang in there. Try working longer on Dev role and see if you are improving every 2 months or so. Getting or not getting a Google swe position is no way the only scale to gauge how good of an engineer you're. If you improve, you could start interviewing with Google again after 6 months or so.
I was thinking same way, but wanted to get reassured by the crowd. I'm very new to the US culture/career scene...