One line of thought here is that of existentialism. Philosophers from Aristotle to Aquinas and beyond have thought that there is a human essence, an essential human nature; and that actions flow from this nature. 'To be' a human being is 'to act' in certain characteristic ways and to have certain dispositions to act. Our essence is intrinsic to our existence; it's like the blueprint from which we are made. The phrase for this is that our essence precedes our existence.
Existentialists such as Sartre reverse this relationship between being and action. For them, there is no essential human nature, no human essence, just the endless possibility of defining ourselves through our actions. As we make choices, and as we act, so we become certain kinds of persons : through our actions we come to exist ('to be') the persons we are. As Sartre sees it, our existence precedes our essence. We first exist, then define our nature.
The basis of this philosophy is the assertion that, in Man, existence precedes essence. There is no universal essence of Man, but each man creates his own during his lifetime. In other words, when Man is thrown into the world, he is at first nothing; it is only later that he will become something and he will then be what he has made himself be. To quote Sartre: " L'homme n'est rien d'autre que ce qu'il se fait. Tel est le premier principe de l'existentialisme." [Man is nothing else but that which he makes of himself. That is the first principle of existentialism.]To illustrate this, Sartre says that when you sow the seeds of some vegetable, you know that you are going to get that vegetable and none other. The essence of the vegetable therefore precedes its existence. But when a man is born, you cannot say, since he is a being gifted with reason and a conscience, what that man is going to be. Therefore, in human beings, existence precedes essence.
Since Man is nothing except what he has made of himself, it follows that he is entirely responsible for what he is. (Jacques Hardré, 'Sartre's Existentialism and Humanism', Studies in Philology, Vol. 49, No. 3 (Jul., 1952), pp. 537-8.)
There are endless problems with this viewpoint. But that perhaps isn't to the present point. I have tried briefly to explain a viewpoint in terms of which (in the senses indicated) action can precede existence or being. I am only trying to make sense of the viewpoint in a rough sketch, not inviting you to accept it - or to reject it either.
Sartre's 'Existentialism and Humanism' sets out the viewpoint briefly and clearly. As one expands the brevity the clarity tends to reduce.
Jean-Paul Sartre, Existentialism and Humanism.
ISBN 10: 041331300X / ISBN 13: 9780413313003
Also online at : https://www.marxists.org/reference/archive/sartre/works/exist/sartre.htm
Jacques Hardré, 'Sartre's Existentialism and Humanism', Studies in Philology, Vol. 49, No. 3 (Jul., 1952), pp. 534-547.
Mary Warnock, Existentialism, London : Oxford University Press, 1970.
There is longer, more recent, more complex work but these basic texts will provide a first orientation.