I adjusted your question from asking about "a" protagonist to "the" protagonist, since, within one written work or play, there is generally only one protagonist. Just to be sure you understand what the term protagonist means, I've included a link below. In short, this Enotes link describes the protagonist as:
the main character...around whom the events of the narrative's plot revolve and with whom the audience is intended to share the most empathy. In the theatre of Ancient Greece, three actors played all of the main dramatic roles in a tragedy; the leading role was played by the protagonist.
So, being a term that originated in drama, it is especially potent when describing the main character of a play, especially a tragedy. This particular protagonist is often referred to as the tragic hero.
In Othello, there are clues before his first entrance in Act I, scene ii, that give the audience the impression that Othello is the play's protagonist -- the title of the play for one. Also, in Act I, scene i, all of the ruckus between Brabantio, Iago and Roderigo is about the actions of Othello, and Iago sets his role as villain (or antagonist to Othello) up:
Though I do hate [Othello], as I do hell's pains,
Yet, for necessity of present life,
I must show out a flag and sign of love.
Act I, scene ii is the first entrance of Othello. He does set up, in this scene, some of the reasons he is the protagonist in his first speech, which begins at line 13:
My services, which I have done the signiory
Shall out-tongue his complaints...
Which, when I know that boasting is an honour
I shall provulgate...
So, in these few opening lines, he has described himself as a man whose deeds can out-speak any man's complaint against him. Yet, he has managed in the same moment to make sure that he doesn't sound boastful, saying that when "boasting" becomes "an honour," he's prepared to go on and on about all his fabulous deeds. And at line 30:
My parts, my title, and my perfect soul
Shall manifest me rightly.
So, Othello is set up as a very noble and highly regarded man, one who seems to be without fault. And though the upshot of the scene is that he is taken into custody to defend himself against the charge that he has stolen Brabantio's daughter, he has acquitted himself a virtuous and noble man, a clear set up for the audience to witness his downfall as a classic tragic hero or protagonist.
And yet, I don't think you can make a case for this one scene "making" him the protagonist. It is the play as a whole that does that.