First many lifeforms don't depend on oxygen (anaerobes), so they wouldn't notice. For aerobes like us, creatures that depend on oxygen, about 3,000 to 10,000 years See: Residence times of some atmospheric gases. Or for another estimate, 4,500 years, see Oxygen cycle (from the 1980s).
That's to reduce the oxygen to zero if there is no input at all, yet all the sinks continue as before. Not a very likely scenario. E.g. if the Earth completely iced over (not that that's likely in the present, but a for instance, it may have happened in the past during "snowball Earth"), you'd have no more oxygen produced, but most of the sinks would be blocked also.
It's hard to find good recent figures, and the figures are surely approximations, but that is good enough I expect to answer the question. Because - the main thing - even if we completely destroyed all green life on the planet - it would have lots of other horrible consequences of course - but the one thing you don't need to worry about.
We'd be able to breath still. Earth is the only place in the entire solar system where humans can breath unassisted. And there is nothing that humans are able or likely to do with current technology that would change that.
And so long as there were a few seeds and some algae etc survive then it would grow back again and the oxygen would hardly dip at all. Plenty of time for trees to grow all the way to maturity before you notice any change in the oxygen levels of the atmosphere.
Also even if you burnt all the trees in the world, all the vegetation, all the green algae, and even burnt all the fossil fuels, you'd not create enough CO2 for carbon dioxide poisoning, or remove enough oxygen to make any noticeable difference.
No way do you want to do this of course :). Loads of other reasons why you don't want to cut down forests or damage the environment of the Earth.