Yes, you can start your seed in it's final container or it's flowering pot, as you call it.
But I would say there is a benefit to starting your plant in a smaller container.
1. Roots will quickly grow to the size of a small solo cup if you start your seed in one. This will help you get a good rootball started for really healthy root development.
2. The roots will fill each container up as you slowly transplant up pot sizes.
3. You get happier plants that drink more and are, imo, healthier.
Transplanting your plant doesn't have to hurt it. Simply ensure the soil is moist and use a butter knife around the edge of the container to loosen the soil, stick the main stem between two fingers with the soil resting against your palm, then flipped your pot and squeeze and pat the bottom. If you have a nice healthy root system the entire dirtball should come out with roots strewn throughout it. Simply fill the next container with your medium and stick your plant in. I've done this with all my plants for my second grow and not one of them slowed down due to transplanting. Hell, I pull seedlings up gently by their stems to put them in different containers and they seemed just as fine...just don't squeeze them too much they don't like that...and I killed one that way, lol.
All I'm saying is unless you gain some sort of benefit from starting in your final container you may want to try transplanting your plants from smaller containers plus I just think it's fun to take a chance to peep at the roots while you're moving them.
My progressions is usually solo cup > quart > 1 gallon > 2 gallon >3 gallon smart pot.