Around 15 million years after the Big Bang, the ambient temperatures was about $24^\circ {\rm C}$, which is in a range where water could be liquid. Could liquid blobs of water be existent then?
PS: I am not talking about water on the surface of any solid planet.

Let's interpret your question to be about whether the conditions would permit blobs of water to remain liquid, whether or not water existed yet. And the answer is No, because the pressure was by then far too low. Basically, space was already a vacuum, just not as hard a vacuum as intergalactic space is now.
It is appealing to imagine an era when the universe was simultaneously dense enough and cool enough for liquid water (and thus perhaps humans) to exist. But alas it is not so. At the time of the creation of the cosmic microwave background, around 370 thousand years after the Big Bang, the temperature was around 3,000K, but the pressure was around $10^{-17}$ atmospheres (see the Wikipedia article Chronology of the Universe, and search for "Recombination").
