HRTIM on the STM32H74x/H75x series comes close to your requirements.
There are capture counters with 480 MHz resolution, i.e. 2.083 ns. I have some doubts though, the external triggers might be sampled at 240 MHz only, and DMA might not be able to store the capture values quickly enough, but I might be wrong, so you can give it a try.
Another idea, if you can find a fast external serial to parallel converter that can convert the input to 16 parallel outputs, which can then be connected to a 16 bit GPIO port of the MCU, where a couple of hundred kilobytes worth of captured samples can be stored and examined at the end of the burst. I don't think that the MCU could provide all the clocks needed for that, so you'd probably need some external circuitry for that. I think it could work with the MCU sampling the parallel port at maybe every 15 MCU clock cycles.