Well, how do you think the government would verify your salary. A 6 month bank statement is a must to get an RP for your family.

if you still dont have a bank statement and have a valid RP, you can go ahead and apply for a visit visa for your family. That doesnt need a bank statement and is also valid for 6 months.

Im sure by that time you can have your 6 month bank statement as well to continue the process of your family RP.