Originally conceived as a sequel to Mad Max: Beyond Thunderdome with Mel Gibson playing the role of 'old Max', the script had undergone changes due to long production process and cast changes so the movie should now be considered a reboot.
Given that the whole movie was written as a sequel to Beyond Thunderdome there are still many direct leftovers from its original form, things such as Max's jacket complete with accurate damage from previous movies. Another remnant is the date on Max's back tattoo. It states it's been 33 years since the apocalypse i.e. the events of Mad Max. Hardy's Max already is in his mid 30's so he'd have to be an infant 33 years before, when events of Mad Max took place. Max was in his early 20's in Mad Max, add 33 years to that and you'd have the 'old Max' that was supposed to be in Fury Road.