I believe what you want is to change the callback in load() to a Promise based API. While changing load() to use promises is rather simple, there are some others changes in your code necessary to make that work as you would expect it to work some of which are described in this blog post. See this version using promises and some explanatory comments.

async function loadUsers(userIds, load, done) {
    const users = [];
    let numberOfLoadedUsers = 0;
    // in order to use await in callback function must be "async"
    // now you must change from "forEach" to "map" as every callback now returns a promise and forEach does not return anything
    const promises = userIds.map(async (userId, index) => {
        const user = await load(userId);
        users[index] = user;
        numberOfLoadedUsers += 1;
        // to show you it is working
        console.log(user, index);
        if (numberOfLoadedUsers === userIds.length) {
            done(users);
        }
    });

    // promises is now an array of promises (one for each item)
    // you must wait until all promises resolve and can then return
    await Promise.all(promises);
    console.log("all users loaded.")
}

// POJ(S)O
class User {
    constructor(id, name) {
        this._id = id;
        this._name = name;
    }
}

async function load(userId) {
    // you must return a Promise in order to make it an asynchronous function
    return new Promise((resolve, reject) => {
        try {
            // load your user here (e.g. HTTP request, read from file etc.)
            const loadedUser = new User(userId, `Testuser-${userId}`)
            // user was successfully loaded -> resolve promise
            resolve(loadedUser)
        } catch (error) {
            // some error occured -> reject promise
            reject(error)
        }
    })
}

function done(){
    console.log("done() called");
}


const userIds = [1, 2, 3];
// test
(async () => {
    await loadUsers(userIds, load, done)
})();

Expected output:

User { _id: 1, _name: 'Testuser-1' } 0
User { _id: 2, _name: 'Testuser-2' } 1
User { _id: 3, _name: 'Testuser-3' } 2
done() called
all users loaded.