Unfortunately there's not a dirt oval available as a track configuration. Few years ago, Scawen did state he is interested of updating Layout Square so that either:
1) There would be a selectable track configuration which would have a dirt area and probably a 1km walled square area as well. Or:
2) One of the track configurations would be a dirt area instead of tarmac in one of those squares between the 4 roundabouts. In this case, you could drive to there from area that is still tarmac. Scawen even made a very early prototype of it.
If that does indeed happen in the future, you could add a dirt oval there. I too would be excited, if Scawen indeed does continue doing that prototype and therefore adds a dirt and maybe that 1km walled square area into Layout Square.
Source, you can find some posts from him on page 1 there about this:
https://www.lfs.net/forum/thread/95714
However, Rony (Eclipsed) has done an AWS 2025 race on Westhill "Dirt" oval. It doesn't have any actual mud/sand, but it's driven 100% on grass. That is probably the closest you can get of having a dirt oval. You can download it from here:
https://www.lfs.net/forum/post/2114363#post2114363 - just download the .mpr replay, open it and save the layout in Shift+U mode.