Live Looping Audio On The Fly?

[NewFutureFantasy]

Hello,
is it possible to live loop audio in Ableton like I do with my Boss RC600 looper pedal. For example, I will repeat a guitar phrase until it sounds as near perfect as my musicianship allows, then using the footswitches with sharp timing I will create a loop of this phrase. I then stop recording and listen to the loop while searching for harmonisations, and when again I find and refine one that sounds good I again use the foot pedals to layer this harmony onto the original loop, and so on until I have a multi-layered sound, all done on the fly as I continually play.
Is Ableton even designed to do this? I am new to Ableton, having just acquired both Ableton Suite and a Push 2. I did wonder whether live-looping would be possible using a footswitch into the Push 2, but I note that the footswitch is a bit slow in triggering Ableton, not the instantaneous action I need and that was on my looper pedal. Perhaps this is because I am using a piano pedal, so is there perhaps another type of footpedal that would work for this? Or would this work with a dedicated foot controller for Ableton? Or could I even control Ableton from the footswitches on my looper pedal? Or is there some other possibility?
Many thanks for your help.

[Greenapples2019]

There's quite a lot of YT videos about looping in Ableton e.g Binkbeats, and tutorials about how to use the looper e.g. Seed to Stage. Ed Sheeran uses Ableton for his live shows so it's definitely possible!