Urgent! (Rented wheelbarrow for day) Adding compost to new garden, can I top dress with 30mm of compost and plant into that, or do I need to dig it in?

I have rented a wheelbarrow just for the day sorry for urgency. I’ve just had compost delivered.

The garden was entirely dense weeds which ive removed, and the soil looks like it’s good condition (some spots looks dry though).

I am planting everything – veggies, flowers, shrubs etc

How do I add compost to the soil? Can I just lay it on top of the soil and then plant/sow into that, will they grow ok?

I also read the roots won’t benefit if it’s top dressed though since roots go deeper.

Or if I need to dig it in, what do I do and how do I do that? I only have a shovel and rake. And I keep hearing about no digging.

Thank you this is my first garden!