The basic point is this:
Neuroscience of free will - Wikipedia, the free encyclopedia
the current work is in broad agreement with a general trend in neuroscience of volition: although we may experience…
But there is more to it, more biologic conditioning from the mere latency of perception, from the fact that space is exposing time as a gradient and much more.
Using “literally” on purpose here: no, we don’t experience the present while conscious and aware. Techniques of breathing and mindfulness and whatever you call them where you lower awareness and dive into subconscious bring you closer to the present blip, but not even that. Only an unconscious state has you immersed in the present but then you don’t experience it anymore, because to experience you require awareness and in an unconscious state awareness is minimal to non existent.
My 2 cents :)