grosso
Is this car a gen2 or gen3?
If gen2 the MAP sensor is only used for fuel cut for over boost, not cold start starting. There no point in testing or changing it. Unless your fuel cut is not working.

 
3SGE Gen3

My 98' Bathurst also has this issue with every startup, if I don't put enough throttle it stalls but the next start goes perfectly.

It sounds like you all need something like this - http://www.okaauto.com/EFI-FPP.html

Here's a much cheaper option - http://www.okaauto.com/Timer.html
I can guarantee that it doesn't start the first time due to insufficient fuel pressure.

Here's a local option - https://www.jaycar.com.au/12v-3a-timer-module-2-seconds-to-23-minutes/p/AA0364 

Maybe try turning it on & letting it sit for a minute to let the oxy sensor warm up, then kick it.

I would not recommend that as it can hit the very hot sensor with a shower of water (condensation). immediately on startup. The O2. sensor gets very hot very quickly.  Been through this fun years ago on Holden and Mitsis.

Admin
It sounds like you all need something like this - http://www.okaauto.com/EFI-FPP.html

Horay for the long weekend.
 
This morning tried jumping the fuel pump again. First time I did this I pulled the jumper before starting the car and the car stumbled on start up. This time I left the pump running waited 5+ seconds and started the car. It fired up fine. I will continue to do this each morning over the weekend to verify that it just wasn't one of those days where it starts fine.
 
Will keep you posted. Cheers!

Jumped the fuel pump again this morning. With the pump running, counted to 5 seconds and started the car. Started great. I will do it one more time tomorrow morning.

👍