That echoes my experience, differing only in detail. Knowledge of God is possible, but not provable to an unbeliever, as you say. I am more sure than merely convinced, I know that I am my Father’s child. Sometimes he sends us things that are more difficult than others, say, kidney cancer. (Problems with relationships can definitely be more difficult than that!) But he knows that I delight in him, and he delights on occasion to toss co-instants to me that are pure fun, saying in effect, “Here, catch! 
” (Here is one such you may not have seen yet, Maggie, being newer here: Moving Day. )