Good question.
They can because the direct observations we make of the early universe place very tight constraints on what the conditions of the very early universe could possibly have been. The conditions are so incredibly tight, in fact, that for many years they were considered to pose a philosophical problem for physics: how was it possible that conditions in the Big Bang were so "finely tuned" that the universe ended up the way it did? If you make a change in even the 50th decimal place, up or down, in any of a number of variables, you get either runaway expansion or nearly immediate collapse.
Nowadays we don't worry about that problem, because the theory of Inflationary Cosmology accounts for that exquisite balance. This model also makes a number of extremely detailed predictions about the Cosmic Microwave Background Radiation, and these preditions have been verified in stunning detail by recent observations with the WMAP probe.
So we're confident that Inflation is reasonably close to the truth. From there, inferring the conditions close to the Big Bang is a matter of straightforward calculation. If those conditions had been ever so slightly different, the universe would look very different from the way it does now.
The microwave background is a rather good record of the b-b conditions.