I've been direct sewing sunflowers about 4 weeks before my last frost date.
But, I'm growing huge heritage sunflowers with big happy seeds (thus they have more energy for surviving cold snaps).
I don't know if they thrive when being transplanted. In the past, I would have said no way. But, now I often see sunflower transplants in the shop (along with peas and beans - also veg I thought were stunted from transplanting) so maybe they don't mind it. The best way to find out what works for you is to try some started in pots and some direct seeded then let us know how it goes.
What I'm growing is Mongolian giant which is supposed to grow 12 feet tall (grows closer to 16 in good soil). It's such a prolific sunflower, I just love it. I grow it next to the hen yard for shade but this year I had to cut a bunch down as they were touching the power lines and they hadn't even gotten to full height.