Expo TypeScript Absolute Path's

babel.config.js

module.exports = function(api) {
  api.cache(true);
  return {
    presets: ['babel-preset-expo'],
    plugins: [
      [
        'module-resolver',
        {
          root: ['./src'],
          extensions: [
            '.ios.js', 
            '.android.js', 
            '.js', 
            '.ts', 
            '.tsx', 
            '.json'
          ],
          alias: {
            'tests': ['./tests/'],
            '@components': './src/components',
            '@views': './src/views',
            '@assets': './src/assets',
          }
        }
      ]
    ]
  };
};

tsconfig.json

{
  "compilerOptions": {
    "allowSyntheticDefaultImports": true,
    "jsx": "react-native",
    "lib": ["dom", "esnext"],
    "moduleResolution": "node",
    "noEmit": true,
    "skipLibCheck": true,
    "resolveJsonModule": true,
    "strict": true,
    "baseUrl": ".",
    "paths": {
      "*": ["src/*"],
      "tests": ["tests/*"],
      "@components/*": ["src/components/*"],
      "@views/*": ["src/views/*"],
      "@assets/*": ["src/assets/*"],
    }
  }
}

Replace both the babel.config.js and tsconfig.json in a new Expo TypeScript project with the above.

The above assumes a src folder with the children assets, components and views.
Import's are now:

import { Fancy } from '@components/FancyComponent', etc.

For more options, see Using Custom Path Aliases with TypeScript

Also note: it's worth installing Expo globally for further development: npm install -g expo-cli.