It sounds like you just got a fob off or the stand in receptionist for the day.
Not knowing what Council you live in I just went to the Sydney Council webpage and typed in Neighbourhood Noise. (I generally find they all list the same State Law compliance information) It opened a word document listing out the various information. If the noise is outside the restricted time then the offender is required to comply with The Protection of the Environment Operations Act 1997 (POEO Act), then take a log of the noise and send into the Council. Being state law all residents and tenants (with signed lease agreements) must comply. My suggestion would be to call again and ask to speak to someone in regards to neighbour noise. Not just the front reception person.
I would start a noise log and go through the councils page & notes regarding noise look through all the various links. Focus on what your specific noise issue is, ie music or barking dogs. Look through the various documents – even if that means state law documents. Make sure you have all the information to prove your point. Also look at other Council pages, some go into more detail about some areas than others and this may be helpful.
I am in WA and we have the State Environmental Protection Act of 1997 which states that for example any music (including music with a defined base) that is audible at that boundary of your property then it is too loud. Any time of the day.
They do mention that if you are in a Strata then to go to the CTTT. I have had discussions with a Strata Law specialist in WA and he said that the Councils and Police have far more power to make them comply with the law than Strata. Sounds silly but he said that was the way it worked.
Don’t give up and record everything. For me all I need is one powerball 