Sunflower shoots are quite large when they emerge from the soil, so from what you have described, I doubt that they are sunflowers. I would guess that they are some kind of weeds that were already in the compost. Where did the compost come from? even if you bought it from a garden centre there's no gurantee that it's weed free. Or the weeds could have already been in the pots of cyclamen that you bought and were transferred when you potted them on.

Hi and welcome to GOY HB can you post a photo and let us all see.
Myron is correct re compost sometimes not guaranteed to be weed free.

are they under a bird feeder as some of the smaller seed could be the cuprit. but to be sure a photo would be brilliant if you do one.
welcoe to GoY fro me too.

I think Myron has it. I have brought home and potted up chickweed, oxalis and many mosses that are already in the soil of the plant I have bought at the garden centre.

I have had to give up using one well known compost which I have used for years, because this year it has been full of weed seed! I even opened one bag which had a hole in it and the seedlings had already germinated in the bag. My seed trays were awash with the same weed. It was just a good job I recognised the leaves of the plants I was trying to grow. Never before have I had to do such extensive weeding in the greenhouse, it was ridiculous and has increased my work load all year.