I have a concrete bridge over a dam that was dipped in the center causing water to pool, freeze and bust out the concrete. The only solution was to "cap" it
The first step was to etch it with Muratic acid so the new crete would get a good hold/bond. Because your's is new that step would not be needed.
The next step is to grind down the areas that are proud of the rest of the slab like around the footprints, to avoid "poke throughs". Use a angle grinder with a diamond wheel or abrasive disc. They do rent concrete grinders, but I don't think that's needed.
Next get some pig fence or other wire mesh with a 2" square or smaller grid. No not use chicken wire, it's not strong enough.
The next step is to determine your mixture ratios, Portand Cement and sand and small pea gravel, IF it's going to be at least 3/4' thick. Thinner than that leave out the pea gravel. As suggested, use a latex bonding agent available at Home Depot or your concrete supplier.
I had a tractor powered mixer that I ran shoveling in the correct mixture. I used 1 shovel of Portland pure concrete, to either 5 or 4 shovels of coarse sand, If I recall.
I wanted a stronger mix than typical ready mix ... 1 part to 3 sand and 3 gravel. Since I wasn't using any gravel, just coarse sand, I needed to change the rations:
Harbor Freight makes an electric mixer that will work for small jobs, but you will need a full time helper to keep it going. It's 1/3 HP which is enough for a small batch like 1 bag of ready mix, but that's about it.
You will need to use screed runners on top of your slab so the cap will be even. I'd use 3/4" thick PT 1 x 3's. and as long as the area you need. I used a 10 ft piece of 2" EMT welded to a 8 ft X 1/1/2" EMT handle with small triangle braces welded back to the 2" EMT. I stood on the center of it in order to bend it slightly. After supporting it off the ground with 2 x 4's in order to put just a slight crown in it so the concrete would drain off. You can screed in either direction because it's round. a small back and forth action worked best, after the majority of it was level.
The biggest issue is screeding the large surface level. You may need to rent a screed or hire someone who is skilled at it or use kneeling pads and a finishing trowel and short leveler. Concrete work requires some special hand tools. A find push broom will work to make a grained texture if you don't want a polished look. after the crete gets somewhat hard... you'll have to experiment to find out when.
Turns out I still had the dang thing:
Also, probably a good idea to watch some You Tubes on pouring a slab....