If the purpose of the (sustained, post-incarnation) mortal life of a Christian could be described as 'learning'; then the nature of this special quality of learning needs to be elucidated.
In our lives we have many experiences, but most of them (perhaps, sometimes - especially for non-Christians, all of them) are unlearned-from and/or irrelevant to our post-mortal future of resurrected immortality in Heaven.
Furthermore, the way in which we learn from Life is distinct from the psychological or neurological processes of 'memory'. In other words, that which we may remember most insistently may not be of ultimate importance; and conversely, we may have learned vital matters despite having never had a memory, or a distorted memory, or having lost a memory.
Deep, intuitive and permanent learning thus reaches forward - so that after death, when all triviality and illusion has fallen-away - this is what remains.
But the vital learning may well be accessible during this our mortal life, by the activity of our real Self (that is our true, eternal and divine self; by which we incarnate into this world as already children of God). And such real learning then constitutes what I have termed the Golden Thread of life.
The Golden Thread is a part of (not the whole of) that which is immortal during mortality. Our purpose in life is to work-on our Golden Thread - to make choices and engage in those behaviours that add to the Golden Thread as we know it now; that is to theosis (that process of spiritual development also known as divinisation or sanctification).
We cannot 'prove' such learning to other people; it cannot (typically) be 'communicated'. The 'proof' (and only proof, in this life) is 'intuition'; and that intuition may be confirmed by the incorporation of material into the Golden Thread (if or when we become aware of it).
To turn it around; if we ask the question - How to do know we are currently engaged in Final Participation? The answer is that we cannot always know, and especially not while-it-is-happening.
But when in retrospect we confirm that some situation has been included in the Golden Thread, then we can be pretty sure that the situation was one of Participation, and if we are conscious of that situation while still 'in it', then we are probably dealing with 'Final Participation.
Why can't we know that we are in Final Participation at the time, or indeed in a situation that will become a part of the Golden Thread?
I think the answer is that reality is a continuous unbroken 'process', and 'moments' do Not have categorical boundaries. Therefore, when we try to establish the status of a cross-sectional 'unit' of life, we are thwarted by the fact that it is not a real category - that moment flowed-from what went before and flowed-into what came after; and was connected-with innumerable other aspects of things.
We are trying to separate-out that which is not truly separate - and that is the problem.
Furthermore, as (real) life goes-on, and the Golden Thread continues to extend (into an unbounded future) - then meanings of events are changed by this new and expanding context. As we develop spiritually (towards greater divinity) our understanding expands, therefore meanings are not fixed.