Why don't chromosomes double in S-phase?
First, chromosomes are composed of an original and a replicated chromatid, called sister chromatids. Chromatids are composed of tightly packed DNA.

DNA is replicated after the end of the S-phase, or in other words, the material composing the two sister chromatids is there. The catch is that chromosomes and chromatids aren't actually condensed yet, the DNA is still completely unpacked at this stage. So in fact, while you do not see actual chromosomes, the material composing them has been duplicated during the S-phase.

DNA condensation occurs two steps later during the prophase, where distinct sister chromatids/chromosomes are then formed from the packing of DNA that was duplicated during the S-phase.