Will heavy clay soil de-compact over time with wood chips?

I am trying to figure out how important an initial tilling is for a lawn to garden conversion in relatively heavy clay soil.

Western NY, the soil has decent organic material already but it is relatively dense – I can’t easily put my finger into it. But grass is growing just fine.

Should I till the garden rows now, or will it decompact over time if I fill the rows with a few inches of compost and cover with wood chips for a couple years?

And I guess related, are there any ideal hand tools for tilling or do I need to rent a machine?

Thanks in advance.