I am posting this so in the future anyone tries a search can find useful info.

Per WestPac ATM Locator, (and kindly posted by Perthite)

Sydney Intl Airport (ATM)
Dpt Gates 8-37, Intl Terminal

Westpac own info already said there is an ATM at Gate 8 - 37, T1. However it does not say Airside or Landside - though in the same page it mentioned its ATM at T2 foodcourt is Airside - so logical deduction is, if not mentioned, it should be Landside. (It only makes sense as Airside is restricted, it needs to be pointed out so people would know.)

The key info was from Goosegreen when he/she identified it being "behind Subway" at the foodcourt. There is a Subway per the T1 map, on the left side of the gate entrance, and there is an ATM symbol right behind it.

Thanks Goosegreen.

I have thought about the taxi issue - that it is understandable about the short trip - they have to make a living and spending time waiting to pick up fares is not the way one can make a living.

The reason I thought the train would be a good option is, the station is just underground, it is a very short ride (3 minutes) with a 15 min service interval - therefore I think it is a good bet - to avoid ground traffic, and to have fixed service intervals that one can hopefully count on.

Again, thanks a lot for everyone who cares to post.