Aerating - how long to wait for.....

When I bought my house in 1990 we joked there were bodies buried in the back yard due to all the hills and valleys. I had wanted to till and smooth it out but lost my job and well, you know how that goes
*Years* go by LOL and we've gathered a few vehicles, one which seemed to stay on the lawn for a couple of years, back and forth. It's a cube van so it's fairly heavy. Last year we noticed some severe ponding in that section of the yard.
This year we're doing a reconfiguration that will keep the van off the yard and hopefully everything else too.
We'd like to aerate the entire back yard and fill in the valleys. I'm removing dirt from another section for a gravel delivery and would be moving that over there.
My question is how long should I wait after aerating before refilling the low spots? I have to time the aerator rental vs gravel delivery vs my time to move the soil (don't want to move it twice!).
I've searched the archives for aerating topics but didn't see one that dealt with adding soil to low spots.
TIA,
Diane
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I can see little point in aerating. Use a cultivator over the whole plot and then rake to level. Then roll and cultivate [and rake]again till rolling leaves no further depressions. Best Wishes.

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