How to repair lows on lawn?

Hi all, I've had a shepard's hut delivered and have chewed up the lawn quite a bit in the process.

I've got a trailer load of top soil ready to use and just wanted to double check what the best process is before making a start.

Here are some photos.

I plan to fill any lows with soil and rake level before seeding. I do not have a roller, would one be necessary or could I use boards / planks?

Any thoughts or suggestions would be helpful as I would like to get the grass to establish sooner rather than later.

Many thanks

 

hi doesnt look that bad to be honest ... i would place the soil in then lightly firm with walking on then rake over as the sub soil I would imagine will be firm already