I don't think it should be that difficult. Project for a weekend hackathon or so. Collect same mouse movement data with a js on your own website if you own anything mildly popular or partner with someone and buy it off, stick it into some off the shelf GAN, job's done. Turing test is broken by modern deep learning

At least the mouse movements themselves shouldn't be difficult to do given a source of data. Simulating that you click on same FB UI elements as real people with same statistical properties on other hand is where you might be lacking the data to do it properly