How can I write a stream to S3 and immediately retrieve a link to read the content back?

I’d like to upload my mp3 file to S3, get the URL to the resource, and send it to the user.

Since the upload may take upwards of 10 seconds, I’d like to stream the upload and allow the user to stream it from my bucket. However, the URL does not seem to be valid until the entire file is finished uploading.

  const passThroughStream = new stream.PassThrough();
  myAudioStream.pipe(passThroughStream);

  const uploadParams = {
    Bucket: bucketName,
    Key: key,
    Body: readable,
  };

  s3.upload(uploadParams, function (err, data) {
       console.log("full mp3 uploaded");
  });

  // Wait 500ms for first few bytes to upload before streaming the file
  await new Promise((resolve) => setTimeout(resolve, 500));
  const fileUrl = s3.getSignedUrl("getObject", {
    Bucket: bucketName,
    Key: key,
    Expires: 120,
  });
  console.log("File URL", fileUrl);

If I click into this URL, I see the following.

I cannot access the resource until the full 10 seconds are finished. I assumed I would be able to access it the moment I began the upload.