Can I set bricks with mortar on a new concrete stoop before it cures?
You can, as long as the concrete will support the weight. A few hours in it'll still be very fragile, especially if your weather is cool. You'll have to feel it out and make a judgement call. Plenty of times we've built basement walls on a new slab the next morning. If we're talking about a single row of brick it should be fine.

Concrete shrinks very slightly as it cures, but I doubt that'll be an issue for you here.