I completed my ACCA 2 years back. And I wrote in numerous times to the Big 4 after qualifying, and even with accounting experience, I got no response to whatever department I have written in to. Sad to say, the Big 4 firms prefer graduates from local uni instead. This is confirmed by some of my managers and even my cousin, who is a partner in one of the Big 4s.
Even if you do get in eventually, the level of learning and exposure varies. I have friends in the Big 4 who says those with ACCA qualifications do not have a chance to audit listed companies, financial institutions, etc. They only get to do SMEs. Priority is still given to those
NTU/
SMU/
NUS grads.
I suggest you think really carefully over this mid-career switch as I really regret studying accountancy sometimes. It is un-interesting and desk bound most of the time.