Solution 1:

The chances of recovering the directory structure & therefore the data intact in its original form are minimal.

Time Machine uses a complex structure of links to files in order to reduce disk usage & preserve the actual timeline.

You may be able to recover specific individual files if you absolutely need something recovered from the history - though I'd be inclined to think that any recovery software will get confused by the linked structure & think it can recover 10TB from a 1TB backup.

If you feel you are safe enough with only a backup from today onwards, with no history, then I would say that would be the best plan.
Start over, let Time Machine make a full fresh backup.