List<Case> caseList = new List<Case>();
    List<CaseHistory> CaseHistoryList = new List<CaseHistory>();
    Map<Id, Date> caseIdMap  = new Map<Id, Date>();
    //Querying Case Records here
    for(Case cs: [SELECT Id, Status FROM Case]){
        caseList.add(cs);
    }
    if(caseList.size() > 0){
       //Querying history for Case
       CaseHistoryList = [SELECT newValue, createdDate, OldValue, CaseId FROM CaseHistory WHERE CaseID IN :caseList AND Field = 'Status'];
        System.debug('CaseHistoryList: '+CaseHistoryList);
        if(CaseHistoryList.size() > 0){
            for(CaseHistory csHis : CaseHistoryList){
                if(csHis.newValue == 'New'){
                    caseIdMap.put(csHis.caseId, csHis.CreatedDate.date());
                    System.debug('CaseHistory Map: '+caseIdMap);
                }
            }
        }
        if(caseIdMap.size() > 0){
            for(Case updateCase : [SELECT Id, ClosedDate__c, NewStatusDate__c, EscalateDate__c, InProgressDate, OnHoldDate__c Status FROM Case WHERE ID in :caseIdMap.keyset()]){
               //Need to populate date field for each status.
            }
        }
    }

Map<ID, Case> caseMap = new Map<ID, Case>();
Map<Id, Date> caseIdMap  = new Map<Id, Date>();

for(Case cs: [SELECT Id, Status FROM Case])
{
    caseMap.put(cs.ID, cs);
}

if(caseMap.size() > 0)
{
    for(CaseHistory caseHistory :  [SELECT newValue, createdDate, OldValue, CaseId FROM CaseHistory WHERE CaseID IN : caseMap.keySet() AND Field = 'Status'])
    {
        if(caseHistory.newValue == 'New' && caseMap.containsKey(caseHistory.CaseID))
        {
            /*caseMap.get(caseHistoryMap.get(caseHistory.CaseID).ClosedDate__c = caseHistory.???
            caseMap.get(caseHistoryMap.get(caseHistory.CaseID).NewStatusDate__c = .
            caseMap.get(caseHistoryMap.get(caseHistory.CaseID).EscalateDate__c
            caseMap.get(caseHistoryMap.get(caseHistory.CaseID).InProgressDate
            caseMap.get(caseHistoryMap.get(caseHistory.CaseID).OnHoldDate__c
            caseMap.get(caseHistoryMap.get(caseHistory.CaseID).Status*/
        }
    }
}