(How) Is it possible to tell the difference between a man made explosive crater and an impact crater?
A manmade crater would leave behind traces of the chemical(s) used to create it (C4, TNT, ANFO, etc.). Assuming the impactor were large enough, there would be traces of shocked quartz or other shocked stone in and around the crater. If the impactor landed in limestone, then there would be significant quantities of quicklime. (I'm purposely omitting thermonuclear devices here.)