I agree with kimmq that what you plan to grow have specific needs. Here's the link to the Cacti and Succulents Forum. Cross-posting there will probably get you some good advice.

It's apparent that you were going for a raised bed here, and although I agree it may not be strictly necessary as stated above, you may want it for aesthetic reasons. You can grow your succulent garden however you want. So yes, you do need some kind of a soil in there to grow them in. Mulch goes on top of the soil - if you use any at all. Research what kind of soil they need. It will not be pure compost no matter what you are growing. To be soil, it needs some of the mineral content of soil. Compost is nothing but organic matter and doesn't make a very good medium all by itself.

If this isn't a huge area you can probably buy what you need in bags - topsoil, sand, compost for example. Whatever you end up buying, examine it first. Find a torn bag or make a small discreet hole to check it out. "Topsoil" can be just about anything and often is.

Oh, and you can quit raking the dead grass away. Put your soil on top of the cardboard and let all that decompose under the ground over time.

Have you calculated how much volume you will need?

Thank you so much for your input. I feel like such a dunce! This has helped me so much. I have now dug a hole and filled with water. So I am waiting and timing now... Just out of curiosity and so that I learn more. kimmq, why do you fill the hole with water twice?

This is the project that I started. @kimmq, I followed your instructions regarding filling the hole with water. It takes waaaay longer than 1 hour to drain. So I guess I need sand. Can you give me advice on what kind, how much, and any tips on adding it to the existing soil? Is play sand the right kind? Any and all comments are appreciated!

Filling that hole with water twice gives you a better picture of how that soil will drain.

Any sand will do. Any idea what the native soil is?

Oh @kimmq, if only I knew!

Where in the world are you?

What does the soil feel like when rubbed between your fingers? A gritty feel would indicate sand while a smooth, pasty, feeling would indicate clay, somewhat the same feeling if you rub talcum powder between your fingers.

I am in so Cal. I went to a mulch place over the weekend. He told me the same experiment with filling water in the hole, only he said if it drains 1 inch an hour, I should be okay. So he seems to think I should be okay. I filled a Mason jar with my soil, and showed him. I am just so confused about how to proceed next.

I so much appreciate your help.

I wish I had some advice for you but I don't know much about growing succulents other than the occasional potted plant. You might want to consult the Cacti & Succulents Forum.

Southern California has mostly clay soils based on my 2 years there back in the 1950's. What did the "mulch place guy" have to say about your soil sample?

Although it may sound counterintuitive adding some organic material to that soil will help with the drainage issue. Some may tell you that you need to add sand but all of the soil scientists I have talked with about this over the last 50 plus years have told me that adding sand to clay is not a good idea unless you really pour it in, or add about 45 percent sand. The organic material will open the soil so water can flow more easily.

I also don't know much about succulents except for a bit of reading and some indoor ones. But I'd also echo the suggestion to check with those who know more succulents and be cautious about adding sand until you know it's okay.

From when I have looked at suggestions about succulents, the comments about drainage and watering have been mostly about making sure the roots are not completely waterlogged (and without oxygen) for extended periods, i.e. drains well. And related to that, comments about what to add to the soil related to 'chunkier' stuff like gravel, even wood chips (but I was surprised about taht, no experience).

I agree with kimmq above that organic material may not cause a problem with water. Yes, it will tend to absorb some water and release it over time, but I like to think of this as a 'buffering' effect - it will still help with drainage somewhat, but crucially, if it absorbs and releases, it's reducing chances that the below-ground area will be waterlogged (or cut off from oxygen). Put more simply, it may keep the soil moist but not soaked, which I understand is the more serious concern.

But ask the specialists )