How to upload all logs in directory recursively with Fluent Bit?

Question

Using Fluent Bit to upload directory:

[INPUT]
    Name      tail
    Path      /var/log/*

Only files directly under /var/log/ are handled, but files in sub-directory are not handled.

I've also tried using the ** syntax, but Fluent Bit doesn't support this.

Is there a way to upload entire directory, with it's sub-directories with Fluent Bit?