How to restore original date and time to RAW file

I had recently encountered a problem saying I needed to format my usb which has some of my life pictures and videos on there, however I used a recovery programme to get them back. Now I have 2 folders saying 'RAW files' and 'Lost files'. The lost files seem to work very well and have the correct date and time, but the RAW files do not.
I wondered if there was any way or programme that would identify when the pictures and videos were taken because surely some of the metadata such as the timestamp would still be there somewhere.
I found it strange too as one video which was 420mb was only 32 mb and when it played it only played for 10 minutes and then cut off saying, "this media maybe incompatible with this format". That is not a problem though as it's 1 video bit just need the time and date recovered from it.
Thank you for any help and it would be much appreciated!

For my clarification, the files with which you are seeing the problem, are they simply missing the correct time and date when viewed File Explorer like this....



or are they also missing detail when you right-click on the file and choose properties, like this...



If it's only missing in File Explorer than that would be because the recovery program copied the file and creation time of the copy is now different than the original.

Thank you for your response. Yes you can right click on the photos and videos but the name as been changed from the previous name to 'recovered...' with number of the file. But I don't mind about that, it's just the time and date which I care about. You are correct about that the recovery programme copied the creation time, but I have kept my old usb unformatted just in case there is another way of getting those files off with the time and date.