Adding a small lawn

[jpdx]

I'd like to remove a couple rotted, weedy raised beds and install a small lawn for my offspring to play in. (Don't worry, we love raised beds and have installed new ones in a more sunny location). I know how to dispose of the wood, but I'm not sure what to do with all the dirt. Can I just spread it evenly around the back yard and plant grass on top? If the dirt proves too compact to spread, do I need to rent a rotor-tiller machine? Assuming I want to get it done this spring (now) for summer enjoyment, should I plant seed or hire someone to install sod?

[RetiredAt63]

Is the wood safe for hugel-culture?  Because then it could be the foundation for the new raised beds.

I would just spread the soil in the low spots where the lawn will go, and then just spread the rest out evenly.  A raised bed shouldn't be too compacted (I know, should and reality don't always match) but you could loosen it with a digging fork first.  Or if it is in good shape, add it to the new beds.