Can something create itself?
Yes, in the sense that a thing can be the solution of its own description, with no earlier moment in which it did the making. Self-reference is a way of solving an equation, x = f(x), with the same unknown on both sides. In 1931 Gödel built a sentence of arithmetic that talks about itself, and it is true, with no paradox in it. Escher's lithograph Drawing Hands shows the shape, two hands each drawing the other's cuff, consistent everywhere and with no ground floor. The universe is a world of that kind, a history consistent with its own records, in which observers recover the rules and build the screen that computes the history containing them. Any other solution of the same condition would be another universe. Earlier and later are orders among events inside the history. The condition that fixes the history holds for all of it at once, with no step counter and no outside start.
Also in Chapter 2: Why Is There Anything Rather Than Nothing?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 37: Why Does the Loop Have No Beginning?watch a universe make its own particles