Shouldn't the array declaration be : let array = [][] instead of let array = [[]] ?

You just need to initialize the array before trying to insert to the sencond level.

let array = [];
function generateField(width, height) {
    for (let i = 0; i < height; i++) {
        if(!array[i]) array[i] = [];
        for (let j = 0; j < width; j++) {
            array[i][j] = Math.floor(Math.random() * 3);
        };
    };
    console.log(array);
    return array;
}

generateField(5, 5);

Please consider these tips

• Do not use array as a variable name because it could produce error in some browsers
• Because Javascript Array is basically linked list there is no need to declare Array in this way let array = [[]]. For sure more suitable is creating new Array and push it to existing Array
• Maybe declare let array = [[]] inside generateField function to make it more reusable because looking at your code I see you want function which creates new Array with n rows and m columns with random numbers and when let array = [[]] is outside your function will be modified every time when you call generateField

Working code below:

function generateField(width, height) {
    let rows = []
    for (let i = 0; i < height; i++) {
        let columns = []
        for (let j = 0; j < width; j++) {
            columns.push(Math.floor(Math.random() * 3))
        }
        rows.push(columns)
    };
    return [...rows] // create a copy of `Array` named `rows`
}

let matrix = generateField(3, 4)
console.log(matrix)

Output

Array(4) [ (3) […], (3) […], (3) […], (3) […] ]
​
0: Array(3) [ 0, 1, 2 ]
​
1: Array(3) [ 0, 2, 0 ]
​
2: Array(3) [ 1, 2, 2 ]
​
3: Array(3) [ 2, 1, 2 ]
​
length: 4
​
<prototype>: Array []