It is not obvious to me that humans can transcend the material universe; indeed my intuition is that this is not possible and indeed the very concept is meaningless. Let me illustrate.
A human individual is such because of the train of associated memories. Yet to create a memory one must perform a physical process that increases entropy. Entropy defines the arrow of time, and time (as Einstein showed us) is wrapped up with space. Space is wrapped up with (or defined by) matter. The illusion of our individuality is a material thing.
Any transcendence would have to take place apart from time, space and matter. But where can this take place? Awareness, pure and unsullied, has struck religious thinkers as a candidate. This is suspect, since awareness is typically about or of something. That is to say, something else.
Yet in the absence of "something else" there is no information. If there is utter unity there is no information because there is nothing to be relative to something else. Information cannot exist without some form of individuation or separation. Mystics of the past have seen this, though they used different terms to say so.
To the extent that we are mere instantiations — made of information — we cannot transcend our substrate. For example, if our universe is resident on a super-dimensional computer (which, some have "proven", is highly likely), then everything we know or can know is fundamentally wrong. The most we can do is guess at the nature of the level above. Indeed, we cannot know how many levels are above us.
Mystics have seen all this, though of course they did not use computers as an example. It seems to me that Kaballah's "Tree of Life" is an attempt to illustrate all this. Of course, like most such statements (including, in my opinion, those of Jesus) it was co-opted and twisted by those who came after.
So where does that leave us? If transcendence is impossible for the individual, what's next? Well, a dog does not know that she is a dog. She just is a dog. Perhaps we could unlearn something from that.