Centipede seed

Buy some on Amazon and keep it moist. Water two times a day very throughly and it’ll start sprouting and taking over in 14 days. I’ve done it in the middle of summer in large bare areas before with lots of success it you have to water it a a lot.

Layering some leaves or other thin layer of mulch over the seeds would help keep them moist.

I spread some earlier this year in my yard. I'm pretty sure the instructions on the bag recommend planting in early spring which is what I did. IMO the amount of success you have is pretty much based on how well the ground is prepared. You need to loosen up the dirt and keep it moist after planting. I had pretty good success with it except in the areas that don't get much sunlight.

I've been told that Centipede is actually the worst grass to have in SLA. Bermuda grows naturally in your yard and will take over if allowed. Zoysiagrass is worth looking into.

What's underneath your new sod?

If by "clay soil", you mean clay, the type of sod doesn't matter.

Think about how good of a base clay makes for any plant.

You might want to consider amending your soil rather than just adding seeds to the same situation.

I cut empty, plastic water bottles in half, cut a few holes toward the bottom for drainage, add potting soil and 3 spoonfuls of grass seed to each.

I put them in a shady spot and water daily until it sprouts. Then, water as needed. I let them grow a couple of weeks. Cut the plugs out with a utility knife and transplant using posthole diggers. Water them for a couple of days.

Quicker and easier than trying to water your whole yard. Twelve hours of direct, La sunlight is brutal on growing grass from seeds.