Yes, simply change the log_files attribute in the relevant targetConfiguration.xml to how many back as you wish & restart log-exporter.
you can also choose & write a specific log-file name if you only wish to export it & then change-back to the 1 value.
example: from the default 1 to 30 (assuming 30 days back is enough for you) or 2020-10-18-151700.log
<log_files>30</log_files>
It'll export your chosen no. of days' log-files from the time you've restarted it.
best change back to 1 once log-exporting backwards is done.
See log-exporter sk122323 > Advanced configuration post deployment section:
https://supportcenter.checkpoint.com/supportcenter/portal?eventSubmit_doGoviewsolutiondetails=&solut...