No Way Out & Not
On the one hand, there is really no way out - and at several levels as well.
First, there is no way out of what I am experiencing right now. I can (and do) try all sorts of approaches, including denial, repression, distractions, etc. But it does not help in the long term.
Eventually, I come to the point where that is abundantly clear to me and the various forms of distractions loose their attraction. Or what I am trying to push away becomes so strong, and my defenses so weak, that it crushes through in a sudden flood. In either case, I am faced with only one option: to face it. To immerse myself in it, whatever it is I am experiencing in the present. To melt into it, embrace it, be with it and then just be it.
When I do this fully, in the realization that there is really no other way out, there is a change. What previously was kept out in the cold, knocking on the door, is now invited into the warmth and melt and soften.
A few weeks ago, I went to a training in a technique that stretches me in several different ways - including some that are definitely outside of my comfort zone. At the end of the first day, there was the experience of being a complete failure, inadequate, etc. For an hour or so, I tried different distractions such as food, reading, music, going for a walk, etc. And it became obvious to me that none of those worked, or had any chance to work. So I laid down on the bed, allowed the experiences fully in, and melted into whatever was there in the present.
What was previously experienced as "other" and a disturbance now melted and shifted. From experiencing myself as fractured and broken, with a strong force coming in from the outside threatening me, everything gradually shifted into a sense of wholeness and deep rootedness, with a current of bliss running through it.
The same is of course true throughout this life. I cannot escape the experiences coming up, nor can I escape whatever life brings up - in the form of any inner/outer circumstances. I have really no choice but to (eventually) face it.
As we go through life, and become familiar with this process of initial avoidance and then melting into it, we also become familiar with a particular pattern. We see that trolls petrify and crumble in daylight. When we allow ourselves to melt into whatever is experienced, the trolls crumble. We allow what was previously kept outside in the cold into the warmth and they mellow out of their fierce and scary appearance.
Continuing beyond death
Going a little beyond our immediate experience, it may also be true that these habitual patterns - now lived in this human life - continue. So even death is not a way out. The patterns continue, and has to be lived, even if it is through another sentient being.
Even awakening to our "true nature" (enlightenment) is not a way out. We still have our human self, and this human self will still go through whatever any human self typically goes through: loss, pain, ups & downs, disease and eventually death. There is no escape from any of these, even in awakening (although it may appear that way before and a little bit into the awakening).
Again, going a little beyond immediate experience (for most of us), we see that there may not even be an escape in the longer run. Even if there is a large scale awakening for humanity, and all beings eventually awaken, and there is some form of "omega point", an enlightened society, a new collective enlightened lifeform emerging, etc., this may just be another phase in the larger cycles. Eventually, it may all start over again, in deep delusion and suffering, again gradually moving through the various levels of awakenings. This is at least what several wisdom traditions say. So even here, there is no way out. Quite sobering, isn't it?
The way out
And yet, to not be onesided, there is also a way out. When we awaken to our "true nature", to and as formless awareness, the Witness, there is a certain liberation. We are no longer blindly caught up in the ups & downs of our human self, we do find a new "ground" which does bring a sense of freedom and liberation from all of this, and also (at least for a while) a current of joy and bliss. But this too may not be "permanent", at least of the cosmic cycles view is somewhat accurate.