If You like i do, prefer Powershell for automation, and want to use Powershell for managing Delphix.
You can start with this, the code will do a REST connection to the engine, and return a Authorization code (if your login are successfull)
$Header = @{
"Accept"="application/json"
"connectapitoken"="97fe6ab5b1a640909551e36a071ce9ed"
"Content-Type"="application/json"
}
$Jason = @{
"username" = <username>
"password" = <password>
} | ConvertTo-Json
Invoke-RestMethod -Uri "<engine url>:<port>/login" -Method POST -Headers $header -Body $Jason
#DemoEnvironment#Masking