You can use Object#values (ECMAScript 2017), but it's not supported by IE (see browser's compatibility).

Note: The ECMAScript 6 specification defines in which order the properties of an object should be traversed. This blog post explains the details.

const map = { a: 1, b: 2, c: 3 };

const result = Object.values(map);

console.log(result);

If you need to support IE, you can use Object#keys with Array#map:

const map = { a: 1, b: 2, c: 3 };

const result = Object.keys(map).map((key) => map[key]);

console.log(result);

I am not sure by map you mean the Map object or an ordinary JS object. However, just for variety I would like to mention that the Map objects are mostly (probably always) stringified like JSON.stringify([...myMap]). So if you happen to receive a Map object in JSON data may be you should do something like;

var myMap = new Map().set(1,"hey").set(2,"you"),
  mapData = JSON.stringify([...myMap]),
   values = JSON.parse(mapData).map(d => d[1]);
console.log("mapData:",mapData);
console.log("values:",values);

You can set initial value as array firstly. See this example:

const [conversations, setConversations] = useState([]); // fianal data is array

useEffect(() => {
    const fetchConversations = async () => {
       const res = await axios.get("/conversations/" + user._id);              
       setConversations(res.data);              
    };
    fetchConversations();
  }, [user._id]);

res.data convert to array by using useState([]) as initial value and convert to object by using useState({}).

And map this array:

return (
    <>
       {conversations.map((conv) => 
            (<Conversations key={conv._id} conversation={conv} />))}
    </>
)