Time machine restoration to mbp

I was downgrading to big sur from Monterey on my mbp ( intel version). When big sur installation media was installing on my harddrive, I received pop up message that the installation media is damaged. I tried several times but the same message keeps popping up. My harddisk was erased before the installation started and luckily enough I backedup my mbp with time machine on an external device. Now how do I restore the backup on my mbp with no macOS?

Thank you