In considering the concentration of a dissolved gas (such as oxygen) in liquid (such as water) there are two separate concepts, the equilibrium concentration and the rate at which equilibrium is approached.
The solubility of gases is higher at low temperature and lower at high temperature. However, there is still dissolved oxygen in water no matter how long you boil it in the presence of air (which contains oxygen). See tables 2 and 3 of The Solubility of Oxygen and Ozone in Liquids. In fact from room temperature (293K) to boiling temperature, equilibrium dissolved oxygen only decreases from 2.5 units to 1.4 units according to the tables.
As reported in Removal of dissolved oxygen from water: A comparison of four common techniques Talanta vol. 41 pages 211-215
Boiling at 1 atm was found to be the least effective. None of the techniques evaluated here lead to complete removal of oxygen. The concentration of residual dissolved oxygen after purging for 20-40 minutes with nitrogen is 0.2-0.4 ppm.
This reference, beyond confirming that oxygen still remains after boiling, gives an idea of the timescale for the approach of equilibrium. The faster you heat and use the water, the more oxygen will remain, but no matter how long you heat the water (in the presence of air) there will still be significant dissolved oxygen.