USB TYPE-C ALT-MODE DisplayPort + USB 2.0, is it supported?
You don't need anything to "covert from to". If you want DP over Type-C, you must have the raw DP output from your system, so there is nothing to convert. You might need however some CC controller that will advertise your port as ALT-MODE DP to an external DP device, which might happen over a subset of PD communication channel. You need to check with requirements on how to advertise the ALT-MODE DP. So having DP might be "critical".

To have USB2, you should have a separate USB 2.0 host controller with D+/D- connected to the same Type-C port. So the schematics is all on your side.