Stephen Hawking, when describing his theory of no boundary conditions for a general audience, draws attention to how the meaning of "beginning" assumes a context where time already exists. So thinking about the "beginning" of the universe would be like thinking about "the beginning of the beginning." So do we have to give up?
No. Say that any mathematical model of time is like the model of a full-size airplane which is flown in a wind tunnel. The mathematical model of time in the wind tunnel would, in this case, NOT be time itself-- just as the model of an airplane in the wind tunnel is not the actual plane. Although we may never fully understand the universe, in the wind tunnel we can at least try.
Relatively new mathematics can be used to build a different kind of "wind tunnel" for understanding time. Here I'm referring to "non-wellfounded" sets as a way to model time-- the best initial reference being Lawrence Moss's entry in the Stanford Encyclopedia of Philosophy (SEP). In this new kind of wind tunnel, the "beginning" of time has more structure.
(And perhaps support new models of relativity, although I can only speculate-- of course.)
Here's a "non-wellfounded set" theoretic model of time:
time = (pointInTime, time)
which on substitution yields
time = (pointInTime, (pointInTime, (pointInTime..., time)...)
In this "wind tunnel" model of time, time is a "stream" (as it's called) of pointsInTime.
"pointInTime" would be the type of the point in time. Usually we think of the stream as comprising real numbers, where one real number for pointInTime could be less than or greater than some other pointInTime, just as one real number could be less than or greater than some other real number. For example--
time = 1, 2, 3...etc.
We next add "nonstandard analysis" to this wind tunnel in order to get
time = (monadInTime, time)
Where monadInTime is a nonstandard monad, which comprises a real number surrounded by a "halo" of nonstandard numbers infinitely close to the standard part of the monad (which would be a standard real number, as above).
A nonstandard monad of time in the wind tunnel would have its "halo" of nonstandard numbers infinitely close to the standard part split into two parts-- the "nonstandardPast" and the "nonstandardFuture," each being infinitely close to the standard part of the monad, which in the wind tunnel is again a real number.
Now in the wind tunnel, we add that the nonstandardFuture is where possibilities exist, and the nonstandardPast is where information exists-- specifically, information in the form of "infons" as they are called in "situation theory." (Again, the best initial references are in SEP.)
This wind tunnel adds more structure to the meaning of "beginning."
First,
time = (pointInTime, time)
On the way to "beginning," time starts out as something that simply exists, ii.e., time = (pointInTime, time)
Next, we exert some invisible force to pull pointInTime apart, in order to separate the nonstandardPast and nonstandardFuture.
Then we add possibilities, which exist in the nonstandardFuture. And information, which exists in the nonstandardPast.
However, in the process of beginning possibilities are initially zero. Whatever would exist in this wind tunnel of proper time would in this case have no possibilities. In other words, it has not yet begun.
Now make the possibilities nonzero, and the particle of system we are modeling in the wind tunnel finally "begins."
And when all its possibilities are zeroed, it "ends." NonstandardPast and nonstandardFuture collapse, and the universe in the wind tunnel ends.
In this kind of wind tunnel, "beginning" is a staged process. "The beginning of beginning" is just the first stage in the process.
Maybe in a hundred or so years, someone (not me) will learn how to design "infomorphisms" (Information Flow by Barwise and Seligman) which connect to General Relativity.