How early can aluminium be produced at first...
It's entirely possible for some alchemist to produce small amounts of aluminum as part of their "chemical tinkering". Whether the substance would be recognized as aluminum, or even an element, is another question along with questions about whether the process is passed along or dies with it's creator, whether or not the process remains a "magic trick", what uses the precious substance is put to, etc., etc., etc.
... and at that point are
Hall–Héroult process technological possible?
The chemistry was known for decades, industrializing the process requires lots of cheap electricity. Without the necessary watts, you won't see the process used.
Could we see both decades earlier, or was they both only developed at the time it was technological possible?
They both were developed pretty much when it was technologically possible.
The chemistry to produce aluminum developed pretty much at the same time chemistry as a whole developed. Everyone was using the new found substances and theories to discover as many elements as they could, so aluminum was identified in that rush. Industrializing the process required electricity and that occurred pretty much as soon as the electricity was available.
You could shave a few years off here and there, but anything earlier is going to require earlier chemistry and electricity.