We may have a terminology problem here.
By “the abs works immediately” do you mean the Teves electric pump - or do you mean that you see an ABS warning light on the dash?
Assuming that you mean the Teves pump, here is a post I did some time ago which describes what should be the sequence of operations -
From your description of the problem, I assume that, as soon as you turn the key to position (II) without starting the engine, the combined pressure warning switch (CPWS - blue/gold job next to Teves pump) detects that the ‘lower switching point’ (2000 psi or less) has been reached (by normal static loss of pressure in the accumulator) and the motor is switched on. The motor will continue running until the ‘upper switching point’ (2700 psi) is reached.
There is a possibility that your accumulator has lost its nitrogen charge so that within a few seconds of the upper switching point being reached, the pressure drops immediately the pump is switched off so that the lower switching point is reached after those few seconds and the pump starts again and so on. The brake boost pressure will not have disappeared after those few seconds because there is still 2000 psi in the accumulator when the pump restarts so the pedal does not ‘go hard’.
Do the simple accumulator test described in paragraph 6 of that post. If you then suspect that the accumulator has lost its Nitrogen charge, you should remove it and insert a blunt probe in to the oil orifice. If the probe enters the sphere then the diaphragm has failed. On a good accumulator, the Nitrogen pressure behind the diaphragm forces it down to block the oil orifice and a probe will not enter.
There are a couple of other possibilities which I will not elaborate on here until you have done the simple accumulator check