Add-PSSnapin VeeamPSSnapin
$Job = Get-Vbrjob -name “Name of your job”
$OptionsToSet = $Job | Get-VBRJobOptions
$OptionsToSet.BackupTargetOptions.TransformFullToSyntethic = $True
$OptionsToSet.BackupTargetOptions.TransformToSyntethicDays = (Get-Date).DayOfWeek
Start-VBRJob -Job $Job
$OptionsToSet.BackupTargetOptions.TransformFullToSyntethic = $False

1. Firstly, it enables synthetic full.
2. After that, it gets actual date and sets it as the day for synthetic full backup.
3. Then it starts the job which according to the previously modified options performs synthetic full backup.
4. When job finishes, synthetic full is disabled again.

This script can be scheduled via Windows Scheduler to run once every two weeks, or once a month. However, for the purpose of backup chain safety, I’d recommend running this script every two weeks, with monthly active full backup option being enabled.