Just FYI, there's some "time lapse" videos on YouTube of sunflowers growing, and some of those videos show sunflowers that are obviously indoors. Here's one. https://www.youtube.com/watch?...

That video was shot in spring/summer (March to July, and I'm pretty sure it's in the northern hemisphere, the UK, I think). If you're growing now in the northern hemisphere, supplemental lighting and timer to simulate spring/summer (lengthening "daytime" light) will be required.

Do you have any knowledge of what variety your seedlings are? How big do they get when grown outdoors?

I aggree with eric, knowing what you have would help! If it is a dwarf variety then maintaining it under lights would be much easier!
Remember also that they have a deep taproot and if it comes into contact with the bottom of the pot it could stunt the root growth and leave you with a shorter specimen! If you do manage to keep it alive until spring its goin to have a stunted root system.
It definitely can be done with artifical lighting! My garden centre has them on display in late spring in bloom, they are normally named 'pacino' and are about 1" tall, very compact with good thick stems and multiple flowers!

My backyard is perty sheltered.just about every yr i have 1-6 some kind of sunflowers come up wild in fall.single head.only grow bout 2-4 ft. One year i had half a dozen for Easter !!!
NOW THAT WAS COOL😎!!!
Now growing inside! I would put each one in a big enough pot with a stake.just in case. And figure out how long to leave lite on so they dont get leggy.IDKWIDTOTEarlier 😕
😎😎😎

After 4 months the sunflower indoors died. It looked like a mutated runt and did grow and got remnants of flower petals, but was only a foot high and stopped growing. Clearly they need extreme amounts of light and warmth to grow properly, but it was nice to try.