A person converts roughly 1 kg of oxygen per day (1, 2) into carbon dioxide.
One Falcon 9 per day converts perhaps 600,000 kg of oxygen per day.
One F9 per day is like a half-million people.
Earth population is 7.7 billion, growing at about 1.2% per year or 92 million per year or about 3 Hz.
So launching one Falcon 9 per day uses as much oxygen as the number of humans born in the next two days will.
Worried? I'm not, but if you are, the Bill & Melinda Gates Foundation as well as other organizations and experts reminds us that the best way to lower population growth is to improve the dire problems of childhood disease and malnutrition. Bring the world up to some minimum level of existence, and population growth will slow substantially, our collective conscience will rest easier, and we can launch more rockets without worrying about oxygen.
The Biosphere is a dynamic and responsive system. Add more CO2 (as we are doing now, way faster than we are burning rocket fuel) and more trees and vegetation grows in the richer CO2 and warmer environment. That in turn makes more oxygen.
But if we use some oxygen, how will the biosphere respond?
That's a really good biosphere question, and definitely askable in Earth Science SE (or possibly Biology SE if carefully written to suit topicality there).
In the mean time, @Hobbes' answer does address this a bit, and the oceans do function to some extent as a reservoir and atmospheric regulator.