Copy the data from the document, not from memory
The first pass is automated, and the software is literal. "Matt" against "Matthew" fails. A hyphenated surname entered without the hyphen fails. A middle name on the passport but absent from the registration form fails at some operators. A date of birth entered in the American month-day order fails.
So before you upload anything, open the document and your account profile side by side and read them against each other. Correct the profile to match the document rather than the other way round. If the profile is locked because a check is already in progress, put the correction in writing in the same message as the documents, so the reviewer has it rather than discovering it.
One mismatch is legitimate and still needs explaining: a change of name. If the ID is in your previous name, send the marriage or change-of-name certificate as a fourth document without being asked.
Submit all three at once
Verification queues are worked per submission, not per account. Sending the licence on Monday, the address document on Wednesday after being asked, and the bank statement on Friday after being asked again is not one wait — it is three waits, each starting from the back. Nobody reorders a queue to reward a customer who answers in instalments.
Gather all three before you open the upload form, send them in one submission, and state in one line what each file is. A submission that can be assessed without a follow-up question is assessed first, and that is the entire trick.
Source of funds: what triggers it
Source-of-funds is a separate and much heavier check, and it is triggered by the shape of the activity rather than by the account. A deposit that is large relative to the account's history, a rapid sequence of deposits, a deposit from an account that is not the usual one, or a withdrawal request far above anything previously paid out will each do it. Guides commonly put the first trigger somewhere around the A$1,000 mark on a new account, but the figure is each operator's own risk policy and is not published — treat any number you read as indicative and ask the operator.
Once triggered, the questions are about money rather than identity, and the review is done by a person rather than by software, so it takes materially longer. A balance can be held while it runs. If large deposits are normal for you, the sensible move is to expect the check and to have the documents ready rather than to be surprised by it — and to read the withdrawal ceilings before you deposit, which is what the high-roller offer we list states up front, alongside high-limit withdrawal casinos.