If the Mac crashes and some files are lost, and there is no available Time Machine backup to restore, you can try professional data recovery software such as iBoysoft Data Recovery for Mac to recover them as long as the data hasn't been overwritten. You should not write any data to it after Mac crashes and lose data.
Have you checked the system report for the Mac crash? It may explain the reason behind the problem. Application incompatibility, insufficient system memory for running apps, heavy usage of CPU, hardware incompatibility, and kernel panic could lead to Mac keeps crashing.
The most terrible thing could be data loss after Mac crashes. The files from nearly the past month disappear from your Mac and there is no Time Machine backup. If you have any online backup of the lost files such as iCloud, you can restore files from it. But if not, try data recovery software.
iBoysoft Data Recovery for Mac can scan for deleted and lost data on your Mac's internal hard drive and external hard drive. You can filter and preview the scanned results to find wanted files, then select desired files to recover and save them to a different location. Download it and try it for free now!
