You might be surprised at how fun and rewarding it is to make some simple things by cutting wood. Just in case you can't find what you're looking for on the market, a few ideas:
A. Put a listing on Craigslist asking someone to build you a simple platform. Say that you'll pay for the materials, and get them to quote a price for the labor. Maybe ask them to deliver it, as well.
2. Find a local maker space. They likely have the tools you'd need. You can rent a pickup truck from a local U-Haul or Home Depot usually. Cutting wood is pretty much the easiest thing you could learn to do in an afternoon. Find out the dimensions of your desired mattress, and for a platform bed, you'll be pretty okay if you play it safe and make your platform 4 inches wider & longer than your mattress (2in on each side of the mattress). Pick up some plywood to go over the frame if you don't want to cut 20 slats--you could, say, make a frame out of just 8 boards, and then screw plywood to the top of it. For the legs, you don't need anything other than, say, a 4" high simple wooden furniture leg[0] to bolt to the platform itself. Then you just bolt/screw it all together.
D. If you really don't want to spend an afternoon of your life cutting some wood, buy a decent boxspring with a wooden frame, then go to Home Depot and pick up 5 or 6 4x4 plain wooden furniture legs[0]. Simply drill a hole for each leg into each of the corners of the boxspring, and add the extra 1 or 2 legs in the middle of the boxspring for centered support (1 if your bed is queen or smaller; 2 if it's a king). Screw the furniture legs into the included tee nut that you hammer into the drilled hole. It won't make much of a mess, and you can have it done in 1 hour. Drilling 5-6 holes is about the only thing simpler than spending an afternoon cutting wood & bolting it together. I did exactly this for my boys' beds, and they even had a blast helping.
[0]: https://www.homedepot.com/p/American-Pro-Decor-4-in-x-4-in-U...