Well, if the new hasn't reached 3" then if you cut at that height then all you can possibly do is nip the new stuff while at the same time cut the old.

I'd say, yes...go ahead, make the usual mowing keeping the grass height no lower than 3".
Cutting it higher; all that does is maybe let you cut it again at that height fairly soon.....rather than later.

Three inches is a good height for a regular cut....it can shade out weed seeds.

Myself, I like to keep it a bit higher....the grass can use the extra moisture that is in the higher blades.

By the way.....if you use a bag by all means place the clippings in the compost pile.....
If you don't have a compost pile.....start one.

Compost given to a lawn early in spring does wonders by increasing the organic matter which helps the lawn retain moisture and feeds the soil. Invites worms to come....and better yet....stay.

So bag it regardless so the new grass gets sunlight?

So bag it regardless so the new grass gets sunlight?

Cut it 3.5 in as to make sure you don't stress the new growth. Bag the clippings this go around. No need for clippings in the new stuff right now and the old sounds like its doin great as is.