I don't think there is any explicit statement in the book to prove one way or another, but I do think there are several pieces of evidence which can indicate the possibility of female Alphas.
When Bernard visits the Director prior to taking Lenina to New Mexico, the Director tells the tale of his own trip to New Mexico:
"I had the same idea as you," the Director was saying. "Wanted to
have a look at the savages. Got a permit for New Mexico and went
there for my summer holiday. With the girl I was having at the moment. She was a Beta-Minus, and I think" (he shut his eyes), "I think she had yellow hair. Anyhow she was pneumatic, particularly pneumatic; I remember that.
If females could not be Alphas, then her designation as a Beta is less important, almost irrelevant. It is highly unlikely that an Alpha would be going out with a woman from one of the lower castes, so then by definition any woman he went with would be a Beta. If, however, there are female Alphas, it is much more significant because he is thus designating her as the lowest level woman he could go out with.
On one of Lenina's outings with Henry we have:
But Henry's tone was almost, for a moment, melancholy. "Do you
know what that switchback was?" he said. "It was some human being
finally and definitely disappearing. Going up in a squirt of hot gas. It
would be curious to know who it was — a man or a woman, an Alpha or
The phrasing here makes it sound like it could be anyone — a man or a woman and an Alpha or an Epsilon, which would include the possibility of a female Alpha.
In the Savage's conversation with the Controller they talk about an all-Alpha society:
"I was wondering," said the Savage, "why you had them at all-seeing
that you can get whatever you want out of those bottles. Why don't
you make everybody an Alpha Double Plus while you're about it?"
Mustapha Mond laughed. "Because we have no wish to have our
throats cut," he answered. "We believe in happiness and stability. A
society of Alphas couldn't fail to be unstable and miserable. Imagine a
factory staffed by Alphas-that is to say by separate and unrelated individuals of good heredity and conditioned so as to be capable (within
limits) of making a free choice and assuming responsibilities. Imagine
it!" he repeated.
And shortly thereafter:
Mustapha Mond smiled. "Well, you can call it an experiment in rebottling if you like. It began in A.F. 473. The Controllers had the island of
Cyprus cleared of all its existing inhabitants and re-colonized with a
specially prepared batch of twenty-two thousand Alphas.
It seems likely that a complete society would include both males and females; thus, if the society was entirely Alpha there would have to be Alpha females.
When the Controller talks about sending Bernard and Hemholtz to an island, we have the following:
One would think he was going to have his throat cut," said the Controller, as the door closed. "Whereas, if he had the smallest sense, he'd understand that his punishment is really a reward. He's being sent to an island. That's to say, he's being sent to a place where he'll meet the most interesting set of men and women to be found anywhere in the world. All the people who, for one reason or another, have got too self-consciously individual to fit into community-life. All the people who aren't satisfied with orthodoxy, who've got independent ideas of their own. Every one, in a word, who's any one. I almost envy you, Mr. Watson."
These people are the ones who are truly able to think for themselves, which would likely be Alphas. And they are described as "men and women", which would mean that there are female Alphas.
In a conversation between Lenina and Henry we have:
"I'm glad I'm not an Epsilon," said Lenina, with conviction.
"And if you were an Epsilon," said Henry, "your conditioning would
have made you no less thankful that you weren't a Beta or an Alpha."
This seems to grant the possibility that Lenina, a female, could in theory be an Alpha.
Lastly, right in the beginning of the book, we are shown that the embryos are separated by caste as soon as they are fertilized:
how, if any of the eggs remained unfertilized, it was again immersed, and, if necessary, yet again; how the fertilized ova went back to the incubators; where the Alphas and Betas remained until definitely bottled; while the Gammas, Deltas and Epsilons were brought out again, after only thirty-six hours, to undergo Bokanovsky's Process.
But it isn't until later in the tour where they are shown the part of the process where the embryo's sex is discovered:
Told them of the test for sex carried out in the neighborhood of Metre 200.
This would indicate that the embryo's sex would not yet be known when separated by caste, which should mean that it is possible for there to be female Alphas.