Nietzsche's main goals weren't happiness or virtue. He was questioning values in a much deeper way, and highlighted this in the passage you quote. Nietzsche was challenging conventional values, especially the conventional morality of Christianity.

Did he think first we should achieve happiness which then will make us virtuous? — deusidex

Nietzsche is a philosopher of contradiction in his most intimate and true essence. Does that make him hypocritical? No, because it is his awareness of this fact that would make him write and be "worshiped" as one of the greatest representatives of postmodern philosophy.

In "The Gay Science" - 1882 - Nietzsche would state:

“To live is to suffer, to survive is to find some meaning in the suffering!"

and in the same book, he would say:

“And we should consider every day lost on which we have not danced at least once. And we should call every truth false which was not accompanied by at least one laugh.”

Nietzsche affirms with these passages that life is, in one last analysis, malignant, painful, and full of suffering, however, when we make sense of this suffering, we can get through the falling, dancing - aka, your answer to your greatest pains and sufferings, shouldn't be one of defeat and regret, and yes, one of happiness, because, what better way to fight against the angst of life, than through happiness in the worst of hells that it had caused to you? -.

But do not mistaken his words about "virtue" and its meaning. Nietzsche refers - when he uses "virtue" - to the long-lost virtues of the "nobles", and that over the millennia - more recently, thanks to Christianity - was supplanted by that of the "slaves".

Reading that call to be "physiological" is not presented as something that is given upon desiring it. The instinctual quality he desires is not a simple result of removing certain impediments. He kept referring to all this work that had to be done. I think he was sincere in calling for a science. I don't know what he meant by that.

It wasn't the takeaway message for the Nazis!

Found this just now....

https://www.google.com/amp/s/bigthink.com/amp/man-doesnt-want-happiness-says-nietzsche-2604504037

Not sure of the writer’s merits, but seems accurate from what I skimmed.

"The most general formula on which every religion and morality is founded is: "Do this and that, refrain from this and that--then you will be happy! Otherwise..." Every morality, every religion, is this imperative; I call it the great original sin of reason, the immortal unreason. In my mouth, this formula is changed into its opposite--first example of my "revaluation of all values": a well-turned-out human being, a "happy one," must perform certain actions and shrinks instinctively from other actions; he carries the order, which he represents physiologically, into his relations with other human beings and things. In a formula: his virtue is the effect of his happiness."

Did he think first we should achieve happiness which then will make us virtuous? — deusidex

Basicly yes... although there is no 'should', it's meant to be descriptive of how one ends up being virtuous.

His point here is that moralists and religions got the direction of causation wrong. He thinks you do not become happy because you do good, or follow some prescribed moral rules. He thinks you will do good because you are "happy".

Also note the quotes there, happy and virtue will not have the same meaning as it has for those moralists and religions.

"The most general formula on which every religion and morality is founded is: "Do this and that, refrain from this and that--then you will be happy! — deusidex

I wonder where Nietzsche got that idea from.
I grew up in a religious country. The idea above is entirely foreign to me. Where I come from, nobody cared about happiness. People were supposed to "do the right thing" for the sake of "doing the right thing". Happiness or misery never entered the picture.

He was raised in a protestant family. I suppose people back then advised others who struggled with depression to just pray to God and follow what's written in the Bible.

I question whether Nietzsche thought of "happiness" as a guiding determinant of action. I think righteousness would fit better with Nietzsche than happiness, i.e., the eternal affirmation of life is not outcome dependent.

Religion tells us what we must and mustn't do in order to achieve happiness. Nietzsche says that there should be new values (new means authentic, not from outside sources) that do not frame life for us. When the old values are dropped, one has the clarity of insight and from that, right action comes and thus one lives in a natural order which means happiness.

Did he think first we should achieve happiness which then will make us virtuous? — deusidex

I think Nietzsche was analyzing and recounted his revaluation of all values. I don't think he was prescribing that all humans are happy and then virtuous or vice versa. I think he was just saying that some humans can operate in this light?

Did [Nietzsche] think first we should achieve happiness which then will make us virtuous? — deusidex

It's been a while since I looked at the actual texts, but, like Emerson (on whom Nietzsche mirrored his work), Austin attempts to take the gas out of "profundity". The sense that if we are "serious" about our criteria for moral knowledge (as close to certainty), then we will do what is right. Emerson is constantly trying to "lift our spirits" as it is hard to be "averse" to conformity when necessary; what he calls self reliance. Nietzsche's way of deflating this "seriousness" is to call for a sense of joy or happiness (lightness--not the feeling, but an attitude (perspective) in the face of morality). (One thing to keep in mind is that Nietzsche is an analytical philosopher reacting to the tradition--Plato, Kant (why he mentions "imperative"), Schopenhauer, etc.--so he is making a point about their moral theories, but his style has to be obtuse and hinting because you have to take the step to see everything differently for yourself--so to take him as making statements that are true/false (accepted or rejected) rather than as riddles and examples to consider, is to miss the point, and take him too "seriously".)

What Nietzsche is talking about with "happiness" is a point we reach in a moral situation (a specific case) where we must go beyond our deontological morals (not that we stay in this state and aren't just reforming them) when we don't know how to go on, maybe even when to be immoral is to do what is right. That there is a point at which pre-determined, generalized guidelines come to an end. Then we are turned on ourselves and what we do defines us (our humanity as it were). We are responsible for how we act, beyond our knowledge of what to do (but extended from it). Wittgenstein will speak of treating someone as if they have a soul; Emerson will say that character is higher than intellect.

So the image that happiness leads to "virtue" is that acting (when necessary) from this place of being responsible to other's moral claims on us, intelligible for our actions, read by them, that that reflects on us, our character--"virtue" in Cicero's sense (an ethical moral epistemology). Not that we will do the right thing, but that (sometimes) what we do makes us who we are ("physiologically" is Nietzsche playing off the "body" (who we are, and are to be) in contrast to the "mind" (seeing moral skepticism as an intellectual problem); which Wittgenstein echoes when he says "The human body is the best picture of the human soul." PI p. 152).