No.

And as I recall, there is a penalty for filing without one, at least there was years ago.

Does the tax amount change if you just remove the dependents from the return?

There are no exemptions and the credits require an SSN so I'm curious.

You can only e-file if the dependents have Individual Taxpayer Identification Numbers (ITIN).

You can't get an ITIN if you're eligible for a SSN.