If you "run the clock backwards" using the Friedmann equations, you can avoid a singularity; you just need the pressure and energy to behave in the right way when the Universe was very hot and dense. The catch is that "the right way" in this case means that ρ+3p<0; in other words, either the energy density or the pressure (or both) have to be negative. No conventional forms of matter are known that satisfy this inequality, so unless something really strange was going on in the early Universe, there must have been an initial singularity. (Or, more plausibly, there was a time in the early Universe where the spacetime curvature was sufficiently large that the laws of GR as we know them did not apply.)
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