Big Sur Installation Problem Stuck In Recovery Due To Insufficient Space To Install

Hi,

I've a problem. I decided to upgrade my 2013 Macbook Air to Big Sur today. After I downloaded the OS, I couldn't Install the OS because of insufficient space, I needed a further 2GB.

I decided to free up some space, alot of space at that, just to be sure. I removed something like +25GB. I was able to install the OS.

After installation, my Macbook attempted to reboot but continuously just turned itself on for a few seconds, then immediately of and kept repeating the cycle.

It eventually said the installation had failed.

It prompt me to use Target Disk Mode, but I don't have access to another Mac ATM.

I was able to launch into safe mode, where it gives me a few options, including reinstalling Big Sur. I attempted to reinstall Big Sur but now it's saying I have insufficient space to continue with the installation.

Can anybody help me with this matter?

I'm able to access Disk Utility, however I can't access/modify any of my personal files saved on my Macbook, at least I think I can't.

Would deleting the APSF data help? Or am I just gonna ruin the entire laptop by doing so? At this point, I don't mind loosing personal applications and files.

I stupidly didn't have time machine set up.

TIA.