Your carrots look wonderful!
I hydrate jiffy pellets and then put a seed in each one. I put them under lights in the house until they have a set of true leaves. My grow-shelf set up has ventilation fans that blow across the seedlings. I turn the fans on once I remove the humidity dome as soon as I see some sprouts. I use a little apple cider vinegar in the water to keep the jiffy pellets from getting moldy.
Once I see a set of true leaves, I rip out the bottom of the jiffy sac prior to planting. If I don't, the carrot will grow through the bottom of the sac, but it'll have a weird 'waist' where the sac was restricting it. I'll either plant the whole thing in the SiP with a bunch of his friends or if the SiP isn't ready, I'll plant in solo cups to hold until it is ready.
That's what *I* do. I know other folks have very different experiences and do things differently, so I'm hoping folks will jump in and share their system with you. I haven't had luck direct sowing, but for other folks, that's the only way they do it.