I think the easiest way would be to add in the file extension.
for example, take the file "0351", you add a ".png" to the end so it looks like "0351.png", and check if it opens in blender.
If it works, you can batch change the file extensions using cmd in windows.
Search for cmd in the start, and open it
Go to your folder where these files are located and copy the directory
cd (paste file location)
Please mind the space after "cd" in the above command
It would look something like this, but replace the "D:\DATA\Test" with your copied location
If you have the files stored in a different drive (if the files are not in the same drive as you have installed windows on), you need to perform an extra step and type in the letter allocated to the drive. You can find it in "This PC" (search in start)
In this example, it's "D"
so, if yours is stored in another drive, in this example "D", type in the below command and replace "d" with the letter allocated to your drive.
it should look something like this
if you have everything in the same drive as where windows was installed, skip this step and move on to Step 5
type in or copy-paste
ren *. *.png
How it works
ren = short for rename
*. = the original extension, since we don't have any, leave it blank
*.png = the extension we want to change it to)
and your problem should be fixed
If you are using PowerShell in windows, please use the commands provided by Markus as a comment below this post