Make POST https request in AWS Lambda without waiting for response

Question

I am trying to make an https request (API gateway call to other Lambda) in my AWS Lambda function with Node.js, but without waiting for the response, so when the data has already been sent to the other Lambda (and starts running), my first Lambda stops running.

What I've been trying to do is the following code:

await new Promise((resolve, reject) => {
    const options = {
        hostname: 'example.com',
        path: '/example/action',
        method: 'POST'
    }
    const req = https.request(options);
    console.log('Request: ', req);
    req.on('error', error => {
        reject(error);
    });
    
    // Send data
    req.write(JSON.stringify(data));
    
    req.end(() => {
        // This is where (in theory) request has been made, and no response received
        resolve(req);
    });
});

It results in a timeout issue, due to resolve is never called.

Any ideas?