In your API Gateway service, install the Firebase Admin SDK for server-side verification.
```bash
npm install firebase-admin
```

Initialize the Firebase Admin SDK with service account credentials.
```javascript
const admin = require('firebase-admin');
const serviceAccount = require('path-to-service-account-file.json');

admin.initializeApp({
credential: admin.credential.cert(serviceAccount)
});
```

Create a middleware function to verify Firebase ID tokens.
```javascript
const authenticate = async (req, res, next) => {
const idToken = req.headers.authorization?.split('Bearer ')[1];
if (!idToken) {
return res.status(401).send('Unauthorized');
}

try {
const decodedToken = await admin.auth().verifyIdToken(idToken);
req.user = decodedToken;
next();
} catch (error) {
return res.status(401).send('Unauthorized');
}
};
```

Use this middleware in the routes where authentication is required.
```javascript
app.use('/api', authenticate, apiRoutes);
```

Include user information in the headers, context, or payload while forwarding the request to other microservices.
```javascript
const forwardRequest = (user, serviceUrl, reqBody) => {
const options = {
method: 'POST',
headers: {
'Content-Type': 'application/json',
'User-ID': user.uid,
// Add additional headers if needed
},
body: JSON.stringify(reqBody),
};

return fetch(serviceUrl, options);
};
```

Make sure each microservice reads the user information from headers and does any needed checks for authorization and business logic.

Install the Firebase Admin SDK in each microservice that needs token validation.
```bash
npm install firebase-admin
```

Initialize the Firebase Admin SDK with service account credentials.
```javascript
const admin = require('firebase-admin');
const serviceAccount = require('path-to-service-account-file.json');

admin.initializeApp({
credential: admin.credential.cert(serviceAccount)
});
```

Validate the ID token in the relevant service methods.
```javascript
const validateToken = async (idToken) => {
try {
const decodedToken = await admin.auth().verifyIdToken(idToken);
return decodedToken;
} catch (error) {
throw new Error('Unauthorized');
}
};
```