Opportunistic

In first year there are 5 stages of Maths units:
MATH1111 - Introduction to Calculus - This math unit is like super-fundies and intros people to basic uni maths from a gen maths or no maths b/g and helps them to take on MATH1012 and 1014 in sem 2.
Fundamentals - MATH1011, 1015, 1012, 1014 - for people who did Mathematics
Regular - MATH1001, 1002, 1003, 1004, 1005 (only do 4) - most people do this, they're for people who did Maths Ext 1
Advanced - MATH1901, 1902, 1903, 1905 - for people who did Maths Ext 2
Special Studies Programme - 1906, 1907 - For people who got a good ATAR and did well in MX2 - You pick 1906, 1907, 1902, and 1905/1004 (this is because to get into second sem SSP you have to have done first sem SSP and 1902 and have done well)

Not all maths units have to be taken at the same level.

Afaik, you NEED regular or above to do engineering.
But I'm not sure because I never had a problem as I did advanced.

Just go to USyd or UTS then (I think) and do whatevs
but if I was you I would want to get at least 92+ in mathematics
and then do the regular maths units at usyd
and pass them
#yolo

My recommendation would be to study MX1 if possible.

If that isn't possible, I don't think a bridging course will help, you should just try really hard at uni
I don't really know what you should do otherwise :/
What is your closest uni? What suburb are you located in?