Congratulations to you.
In regards to the EEA family permit alone - take a look at the EEA family permit sticker. There should be two fields, one of them labeled "Valid from", and the other one labeled "Valid to". These two dates determine your eligibility to enter and necessity to leave the UK. In general, if you enter the UK sooner than your visa validity, you are likely going to have problems, ranging from simple questioning at the border up refusal of entry. See here for more details about
EEA family permit.
However, since you are an Argentinian and can travel to the UK visa free, your visa free status takes precedence over your EEA family permit (for the purpose of entering the UK). You can enter the UK at any time. The EEA family permit (or its validity) determines your other rights which it provides above the scope of regular Shengen visa (type C), such as your eligibility to take on employment.