Hi Lauren B

There are two ways to solve your issue.

Option 1:
If you just want to have your issue address then use the following code. In the below code I just made the SOQL result to List<Test_MMA2__c>. Since from your test class that SOQL is not returning any record so this will through that normal error, changing the result to List will solve the issue but you will receive the null return which you need to handle accordingly.
 

public  class MMAResultReportController{
    public List<DOAS_AVS_RESPONSE_LEVEL_1__c> avsresults {get;set;}
    public List<Test_MMA2__c> avsRequest {get;set;}
    public string strRequestID{get;set;}
    
    //public string searchRef{get;set;}
    public  MMAResultReportController(){
        system.debug('####Printing page reference');
        system.debug(System.currentPageReference().getParameters().get('RequestID'));
        strRequestID=System.currentPageReference().getParameters().get('RequestID');
        
        getavsRequest();
    }
    
    public void getavsRequest(){
        avsRequest= new List<Test_MMA2__c>();
        //system.debug ('####strRequestID is: '+strRequestID);
        //system.debug('####Variable is: ' + strRequestID);
        avsRequest = [select MMA_Request_ID__c,MMA_RecordType__c,MMA_Suffix__c,MMA_DOB__c,MMA_Middle_Name__c,MMA_Flag__c,MMA_Sex__c,MMA_SSN__c,MMA_First_Name__c, MMA_Last_Name__c, MMA_Family_ID__c, MMAReportDate__c,MMA_BENE_SSN1__c,
						from Test_MMA2__c where MMA_Request_ID__c =:strRequestID];//                                                                 
    }
}

Option 2
In the Test Class insert a record for Test_MMA2__c with the value MMA_Request_ID__c. Since I am expecting you are using this controller in your Visualforce Page let say Page1 (User your one). Use the following code in your test class. Using this way you don't need to change your main class

@isTest
public class MMAResultReportController_Test {
    
    @istest static void test(){

        Test_MMA2__c tes= new Test_MMA2__c ();
        tes.name='Sample';
        tes.MMA_First_Name__c='John';
        tes.MMA_Last_Name__c='Smith';
        tes.MMAReportDate__c=date.today();
        tes.MMA_Middle_Name__c='De';
        tes.MMA_Request_ID__c = 'Test';
        insert tes;
        
        test.startTest();
        PageReference pref = Page.Page1; //Use your visualforce page name
        pref.getParameters().put('RequestID', tes.MMA_Request_ID__c);
        Test.setCurrentPage(pref);
       	MMAResultReportController ce= new MMAResultReportController();      
        ce.getavsRequest();
        test.stopTest();
    }

    //Some system.assert ....
}

Also as a best practise it is always good to use system.assert making test more robust with the expected values.
Also I see  getavsRequest should be returning either List<Test_MMA2__c > (From Option1) or Test_MMA2__c (From Option 2) based on what option you are selecting

I hope this help for you to take away something moving forward.