I'm studying statistics just at the moment, and for anyone who is curious and has an open mind, the most likely (in a Bayesian sense) reason that the OP has posted this comment is because they do not have access to a single female Senior Software Engineer who they feel meet their requirements. (This is more likely than an alternative explanation such as that the best candidate for the position OP wishes to fill is female, but OP refuses to hire a female.)

For anyone who is curious and has an open mind, since women are half of the population and attain a large number of degrees (as opposed to many decades ago when they were not allowed in education at all), why does OP not have access to female candidates OP feeels meets their requirements?

Since I am studying statistics, I looked up the answer in a lecture about women, collected in a book called the Past, Present, and Future of Statistical Science[1]

There are interesting comments about sexism within the science of statistics, for example:

Thwarted employment search after college
Having discarded high school and college teaching, actuarial science, and
medicine, I sought employment after college graduation in 1960. I was aware
of only two methods to find a job: look in the newspapers’ “Help Wanted”
sections and talk with employers at job fairs on campus.
The newspaper route proved fruitless. Younger readers may not be aware
that newspapers had separate “Help Wanted Female” and “Help Wanted
Male” sections until the late 1960s or early 1970s when such practice eventually was ruled to be illegal sex discrimination. In 1960 advertised positions
using math skills and interest were in “Help Wanted Male,” and I assumed
that it would be futile to apply. Job interviews on campus with employers
played out similarly; all positions were segregated by gender and all technical
positions were for males. One vignette, among many, illustrates the employment culture for women in the US in 1960.
When I registered for an interview on campus with IBM, I was required to
take a math aptitude test. The IBM interviewer commented that he had never
seen such a high score from any applicant and offered me either a secretarial
or an entry sales position. I countered that I was interested in their advertised
technical positions that required a math background, especially given my score
on their math aptitude test, but he simply said that those positions were for
males. End of conversation.

-

Clearly, this process explains why OP does not have access to female applicants he feels are qualified. Perhaps OP is judging the history of candidates and applicants, but many other people judged their gender in the past when excluding them.

What should OP do?
Of course, OP can't force others who excluded women from going back in history and including them instead. Is there anything OP can do now to try to rectify the injustice?

I think that one thing that OP could potentially do is follow the process outlined in the company. He could hire a woman for the role.

I think it is the right thing to do in OP's situation and given the history of the industry.

[1] if you search for this title on Google one of the top results is the full PDF so I think it's okay to post it here: https://higherlogicdownload.s3.amazonaws.com/AMSTAT/71a758c7...