You have made a very valuable insight, Lampokey (welcome BTW!), but the “always” of the timeless singularity-type-object is a little different to the “always” proposed by Steady Staters. In their model, there is no “place” in the universe where time has no meaning - the “line of time” stretches back infinitely. In currently accepted cosmology, the line stretches back to a certain point and then kind of “changes direction” so that it isn’t time any more (although it might be something “timelike”).
The main reason for discounting the Steady State theory is the discovery in 1929 by Ed Hubble that all galaxies are moving away from us (light from every observed galaxy is red-shifted, ie. lowered in frequency like the sound of an ambulance moving away from you), whereas the Steady State would predict a random spread of stationary (no frequency shift), approaching (“blue-shifted”, like the ambulance sound approaching) or receding (red-shifted) galaxies.
This took quite some time to become accepted, during which Steady Staters like Fred Hoyle ridiculed the idea by asking “What, so you expect us to believe that the origin of the universe was some king of Big Bang or something?!”. This term of lighthearted derision gradually became the standard nomenclature - a shame IMHO since it misleadingly implies an “event” (which requires time!) rather than a “place”.
Incidentally, Steady Staters haven’t given up the ghost yet. However, they admit that the expansion of the universe is a real observation (illusory or not) which must be explained by any new theory.