SELECT 
  company_id, 
  secure_storefront 
FROM 
  cscart_companies 
WHERE 
  secure_storefront RLIKE '^(www[0-9]*.)?archive.barnlight.com'

Query time 0.00042

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_companies",
      "access_type": "ALL",
      "rows": 1,
      "filtered": 100,
      "attached_condition": "cscart_companies.secure_storefront regexp '^(www[0-9]*.)?archive.barnlight.com'"
    }
  }
}

Result