You can only choose one of the verification options available for your listing.
If the only option is a postcard, you need to ask for one.

The verification methods available to each listing will depend on how much trust does Google has on your phone number, website, business existence.

Why does Google do this? To control spam/fake listings creation.

Is there any other method to verify your Google Business Profile?
Yes, there is! Check here how to verify your business on Google – If you are having issues in getting your Google My Business verification code