Here is a quick solution, maybe not the most performant.
  const array1 = [
    { id: 1, name: 'John', score: 124 },
    { id: 2, name: 'Angie', score: 80 },
    { id: 3, name: 'Max', score: 56 },
  ];
  const array2 = [
    { id: 5, name: 'Lisa', score: 78 },
    { id: 2, name: 'Angie', score: 80 },
  ];
  // Index will have -1 if there is no match, otherwise it'll have
  // the index of the first found match in array1.
  const index = array1.findIndex(array1Item => {
    // This will return the index if found, otherwise -1
    const match = array2.findIndex(array2Item => {
      // return array1Item.id === array2Item.id;
      return JSON.stringify(array1Item) === JSON.stringify(array2Item);
    });
    return match > -1;
  });
Instead of stringifying the entire object, if id is unique, you can just compare id as shown in the commented code.
Be advised this could have a complexity of O(n^2) where n is your array sizes. Big arrays may take a while.
Here is it running on PlayCode. It logs index as 1 because the first match is the second item in array1.