I would like to to topdress my entire lawn with a new layer of topsoil
(half an inch) and overseed it, but I currently have dandelions that
are starting to grow. Quite a few dandelions actually. How do I
proceed to coordinate the need to grow new grass and kill off the
dandelions at the same time?

Do I spray the dandelions, topdress, and overseed right away (in that
order but all within a 48 hour period)? Or do I need to wait X amount
of days/weeks after spraying the dandelions before attempting to
overseed (which will bring me to a new problem - by early June my large
silver maple starts dropping its "helicopter" style seeds everywhere on
the lawn sprouting new trees. On a regular "old" lawn this usually
causes 15 saplings to grow (which I kill right away). I can't imagine
how many trees will sprout on a lawn that has 1/2" of fresh topsoil
everywhere. So that's why I'm hoping to have my new lawn growing by
then.

According to the directions for my grass seeds, I'm not supposed to
spray for weeds on a brand new lawn until "at least 3 mowings". But I
won't be spraying the entire lawn. Just spot treating the dandelions.
And this will be on top of 1/2" of topsoil. Will that 1/2" of topsoil
provide enough "buffer" to not harm the grass sprouts from the chemical
spray on the dandelions?

Or do I forget about the dandelions, focus on the topdressing and
overseeding, and only tackle the dandelion issue once they start
blooming? (which will probably start in 3 weeks from now).

Hence my dilemma. If I kill the dandelions now but have to wait 3-4
weeks before overseeding, then the silver maple will get me and I'll
have a forest growing in my back yard. If I kill the dandelions right
now but in the process it prevents the seeds from germinating, then
I'll have a dirt pile on my lawn. If I forget about the dandelions for
now and decide to tackle them when they bloom 3 weeks from now, it'll
create two separate issues. I can't spray them because it'll kill the
new grass. And if I remove them manually, it'll leave my lawn full of
holes and bumpy which is the reason why I'm topdressing in the first
place (to even out the bumps).