How to check Uber Trials of Ascendancy progress?
As of 3.0 there is a way to check the progress outside of maps.
Once you have activated the waypoint in Aspirants' plaza you will have a new icon on the world map:
Once in the Aspirants' plaza, the new "Labyrinth activation device" will show your current progress:
As I show in the image, by going with the mouse over one of the icons will show you which trial it refers to.
No. It's not possible to check without finding a trial in a map. This is a pretty common complaint and will probably get addressed at some point, but not yet.