Recovering system software situation from a earlier date

I have a problem with the Backup on Time Machine.
Already for some days I get the message that "Backup was not performed because an error occurred while copying files to the backup disk"

It is not unlikely that I removed by mistake, an essential system file when removing files in a recent clean up?

In Windows it was always possible to go back to a selected date and replace the system files with the situation as it was on that earlier date. Using this Windows-capability has solved for me some serious problems.

Time Machine informs me that the most recent Backup has been performed on July 4th.
So if I could go back to the system files situation before July 4th I might be able to solve this back up problem with Time Machine?

Can anybody help me in this matter?

Thank you on beforehand!

Harry