No, this doesn't make any sense. Whatever number of dimensions the universe has, it has, and has always had.
While the universe *may* exist in higher dimensions curled up at a size below the Planck Length, the observable universe as it exists for our practical geometry exists in four spatial dimensions and one temporal dimension. The geometry of the universe is hyperspherical. It exists as a finite, unbounded surface volume embedded along a hyperspatial axis. The existence of particle physics requires atleast this many dimensions to work properly, and particles have existed since Time Zero. A universe that "began" with fewer dimensions than we currently recognize just wouldn't work.
"all within the first milliseconds of our universe"
The First Cause of the universe was a singularity, which possesses values of zero in all dimensions the universe may possess. This includes the temporal dimension, and so a singularity can possess no duration. This means that the spatial size of the universe has existed as a positive, nonzero value for its entire duration, all the way back to the mathematical limit of Time Zero, which also means that however many dimensions the universe possesses now, it possessed then. It had to, for even merely the math to work out properly, to speak nothing of the physics.
Orac - "Generally though if someone invokes string theory, I tend to go and hide!"
String Theory is a brilliant piece of work, and may in fact describe the subatomic world accurately.
This, however, has to do with particle physics, and describing energy particles as vibrations of space in higher dimensions, so applying concepts of 1- or 2-dimensional entities doesn't apply anyway. And, it doesn't imply in any fashion that the universe *itself* even existed as any sort of "string"
Addendum: Jerry Lee - "Physicists seem to be . . . adept at some combination of philosophy and speculation. I do not see how discovery of a possible 4th dimension implies the universe might have started out with much less. "
Now that I've actually gone and read the article, I find myself in complete agreement, especially with your second statement.
Plus, a one-dimensional universe cannot by definition be unbounded. The minimum number of dimensions for an unbounded universe would be two dimensions (a one-dimensional line embedded in a planar dimension), so the very concept of a one-dimensional universe is nonsensical to begin with.