You can't use the soft mats as a diving platform, nor can you get fully out of the water on them. (A concern if water is cold.)
Building an offshore platform is fairly straight forward: You need dimension lumber and either several styrofoam blocks, or at least four 45 gallon plastic drums. Your local marina will have barrels in the fall that propylene glycol came in, used or winterizing RVs and boats with plumbing. Usual price is about $20.
There are various designs, but keep the bungs out of the water. Expansion and contraction of the air inside will cause them to water log. Note that a barrel supported platform tends to ride too high, which is really hard to get on to. Building in multiple levels makes them more fun with more games possible.
Edit: Multiple levels has other advantages:
It makes the platform more visible. The platform (and kids) are less likely to be clobbered by someone in a motor boat. This also makes the platform easier to find if it breaks it's mooring, and less of a hazard.
Provides an area of shelter from brief storms, a place where a parent can get out of the sun to read. A place to store snacks, bottled water.
A place to mount standard lifesaving throw ring and rope, and reach pole.
A place for higher dives. (Stability becomes a concern. Sudden lurch in a wave, and someone's dive meets the deck instead of the water. More mass under water. Barrels half full of sand upright. You want the roll period to be long compared to human reaction time.)
Other safety thoughts. Not all of these have to be implemented. Depends how much use the platform gets in the summer.
Some part of the platform with railings. They don't have to be continuous, nor meet the 'ball test' for toddler proofing. (Toddlers are unlikely to be on here) But it gives a place to lean and watch. This becomes more important as wave size increases.
Some shelter from the wind. In early spring the water can be quite chilly. Having a place to be in the sun and out of the wind can make it easy to recharge for the next plunge, or for the swim back to shore. This can be as simple as making the railing on one corner have 2 sheets of plywood
If you have two anchors, or have a spring onto one anchor line and a cleat at the other end of the raft, you can control the raft's angle to the wind.
Towing point for bringing it home after it escapes.
At least the edges used for launching yourself should be non slip surface.
Edit: I'm not sure if it's possible to keep drums from water logging unless perfectly sealed. In which case they will oil can like crazy as temperatures change. It may work better to put a pin hole in one bung, to led it breath, and keep that bung out of the water, but design your raft so that you can drain the barrels in winter when you do your fall maintenance.
It may be possible to over pressurize them so they don't oilcan. Drill a hole the same size as in a car tire rim, and insert a valve. Most drums are safe to 10-15 psi. Pressurizing the barrel to about 4 psi when the ambient temp is about 60F would keep it from oil canning in winter.