With this .reg I log my user automatically :

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon]
"AutoAdminLogon"="1"
"DefaultUserName"="My User Name"
"DefaultPassword"="My Password"
"DefaultDomainName"="My default Domain Name"

Then I run my script as a boot task and then my wifi is connected and working. I don't use nssm anymore.

For those who might encounter my issue (even if I doubt that it can be reproduced with another config) it resolved it.

The downside is that my PC is longer to be fully operational but I don't care (<2min)