The first
episode (cat and mouse) takes place in the same year AOTC did so we know it
wasn’t a long time. Unfortunately, the EU usually doesn’t specify months so we
can’t know for sure how many weeks passed between AOTC and TCW. It had not be
at least enough for Anakin to recover from his life-threating injuries, marry
Padmé, train with Obi-wan and get acquainted with the 501st. I remember someone from the production team
confirming tcw takes place weeks after AOTC but I couldn’t find a source so
take that with a grain of salt. The only thing that has been confirmed by the
EU is that both AOTC and TCW take place in the same year.