hooks 방식으로 하는 소스도 올려봅니다.

import React, {useRef, useEffect} from 'react';
import {Animated, StyleSheet, View} from 'react-native';

const AnimOne = () => {
  const mySquare = useRef(new Animated.ValueXY(0, 0)).current;
  useEffect(() => {
    Animated.spring(mySquare, {
      toValue: {x: 50, y: 300},
      useNativeDriver: false,
    }).start();
  }, [mySquare]);
  return (
    <Animated.View
      style={mySquare.getLayout()}
      // style={{
      //   left: mySquare.x,
      //   top: mySquare.y,
      // }}
    >
      <View style={styles.square} />
    </Animated.View>
  );
};

const styles = StyleSheet.create({
  square: {
    width: 100,
    height: 100,
    backgroundColor: 'skyblue',
  },
});

export default AnimOne;