It seems the only way to get mms message is to turn on your mobile data. Boo!
Are you sure you don't have any APN settings anywhere?
It should look like this:
https://apn.gishan.net/settings/933_17_consumer_cellular__apn_settings_for_lg_g4.php
Having Consumer Cellular check if it's a T-Mobile phone is moot. You purchased an Unlocked phone, which means any sim card should work. If it is still locked, you need to contact the seller.