When to file my tax return

I feel this is a silly question but I've actually been told different thing when ringing up HMRC so I am hoping for a definitive answer here. I ran a small short lived business which started in may 2024 and is now closed and no longer trading. Now, am I right in thinking that the tax year for running this business is 2024/2025 and therefore, as we are still in this tax year, I am unable to submit my self assessment tax return until atleast April 2025? I know it seems obvious as I feel this is correct but I've been told by someone at HMRC that I can submit now so I just want to make absolute sure before the 2023/2024 online self assessment tax return deadline passes! Any confirmation would be hugely appreciated!

Hi,
If your business started in May 2024 this will be the current 2024 to 2025 tax year. The notice to file the Self Assessment tax return will be issued after the tax year end 5 April 2025.
Thank you