Your requirement sounds a little weird though. You actually want to swim but you don’t like to get wet!?!
If you already have a script in place to trigger the reboot why not using this and extending it with the additional functionality? If it’s not your responsibility you might speak with the adccording colleagues and discuss a solution fitting both requirements.
If you insist on not interfering with an existing script you have to use data Windows already collects such as eventlog entries or registry values or WMI data.
If you already know when the server gets restarted from the script you seem to have in place already the simplest solution would be to get LastBootupTime with CIM and calculate the difference.
Get-CimInstance -ClassName CIM_OperatingSystem -ComputerName 'RemoteComputer' |
Select-Object -Property CSName, LastBootUpTime