There is no need to postulate expansion of space in order to explain redshifts greater than one, in fact you get z=1 for a velocity of just under 180,000 km/s which is quite modest and probably will be achieved by human artefacts[sic] sometime in the next few thousand years.
I am not sure whether you consider tightly collimated clumps of electrons, positrons and protons as “human artifacts”. I do, because they do not occur naturally as far as I know, especially those of the positron variety.
If you do include such things, we achieved such velocities many decades ago.