What is the maximum power you can reach without using machines?
What a great question! I am not sure I have an answer, though!
First and foremost we have to agree on the definition of power, and in what setting you want to find the maximum power. And what do you actually mean by "machines"? Is a human also a machine?
In mechanical physics we often use the power definition P = W/t, work or energy per time, or equivalently P = Fv, force times speed. I'm not sure if there is a law of nature giving an absolute upper limit. Of course, there is not infinte available energy in the world, and so we cannot do infinite work, but I cannot give a number and say "this is maximum".
A human could for example raise a weight of 100 kg 1 metre on two seconds, giving a power of about P = 1000 Nm / 2 s = 500 J/s = 500 Whatt. But there is always someone being a bit stronger, doing the same or more work in shorter time, and so the power is greater.