Question - Query based on WHERE OR

I'm a rank newbie to Postgres & am having a hard time getting my arms
around this.

I'm trying to construct a query to be run in a PHP script. I have an
HTML form were someone can enter either a last name or a social
security number & then query the database based on what they entered.

My query looks like this:

SELECT foo, baz, bar FROM public.table WHERE lastname ~* '$lastname' OR
ssn='$ssn'"

I need to leave the last name a wildcard in case someone enters a
partial name, lower case / upper case, etc.

I want the SSN to match exactly if they search by that.

The way it's written, if I enter nothing for the last name, it returns
all rows, regardless of what I enter for the ssn.

I understand why it happens, but what can I do to return the desired
results?

Thank you.
Mike