Hi everyone,
I thought I would write this for anyone facing a similar situation in the future.
I had my oath ceremony on Friday afternoon (2.30pm) and had a flight booked for Tuesday morning at 8am. I went to the passport office straight from the ceremony and made it just in time before 4pm and managed to apply for a passport. Obviously, they couldn’t find me In their system, so they said that they would wait and check again on Monday morning and call me back if there were any issues. They did want to check my proof of travel and I had to pay extra $110. First thing Monday they called my references and guarantor and passport was ready by 3pm on Monday.