It’s definitely possible! Not super common, but possible - and much more so than it would have been a couple of years ago.
When I was in college (early 2010s) and wanting to enter the field, there was a pretty clear pipeline: four year degree, unpaid summer internships, then apply for a part-time or temp position somewhere, and volunteer somewhere until you get a first job. This is still somewhat of the way it’s done at bigger AZA facilities.
But, interestingly enough, things are changing. There’s two things really driving that. The first is the massive push for increased DEAI efforts in the zoo industry. After the big commitments AZA and many individual zoos made during the BLM protests in 2020, one of the big conversations that started was how inequitable zoo hiring and especially internship programs are. Requiring four years degrees and large amounts of unpaid labor before getting a job - and paying poverty wages once someone gets that job - biases success entering and staying in the zoo field towards people with generational wealth. I honestly didn’t think the advocacy that stemmed from those discussions would do much, and I’ve been very pleasantly surprised to see that I was wrong! There’s a been a lot of real movement towards creating paid internships and making hiring requirements more equitable. It isn’t happening everywhere, but I know it’s becoming more and more common (and last year there was a ton of presentations about this on the AZA annual meeting schedule, which is a huge deal). The other thing that’s happening is less formal, but equally fascinating. I’ve been present for a lot of discussions about how there’s a disconnect between what zoos are hiring for (formal education, complex resumes) and what skills the job actually requires. It seems like it’s easier to train people to work with animals and learn their behavior than it is to teach people practical skills like how to do manual labor without hurting themselves and operate heavy machinery. I’ve seen some discussions of how some of their most successful new staff have come from adjacent industries or even just other “blue-collar” jobs that involve similar types of work, regardless of what their academic background is. Which is great! Because that adds to equity and diversity of staff across the industry.
To start off the rest of my answer, there has to be a disclaimer that I’m not in hiring, so I can’t say for sure what will get you a job (and while I’ve volunteered and interned, I have never been formally hired as staff by a zoological facility). So my advice for the rest of this comes from watching and listening to a whole ton of industry folk for the past decade or so, and from what I’ve seen my friends do that’s been successful to get jobs in the field.
In terms of experience, the best thing you can do - and I hate to say this, because it does require a level of privilege to be able to do - is volunteer somewhere. It doesn’t have to be at a zoo. Anything that will give you some animal experience for a resume and references will be valuable: shelters, vet offices, riding barns, farms, even 4H. You need to be able to demonstrate that you’ve worked around a variety of species (even if they’re all domestic) and have people who can speak to the fact that you’re diligent, attentive to detail, and have common sense about things like safety protocols. If you can’t volunteer, try to find a job in any of these areas with similar skills. Or where you can learn them! Say you can’t get an animal care job, but you’re good at phones and people - you could get a desk job at an animal shelter, and help out with cleaning and animal enrichment when possible. Boom! Experience!
It’s also important to learn how to shape your current job experience to an application, which is something I can talk more about and maybe pull in advice from folk actually in hiring for. There’s a ton that can be applicable to animal jobs. Office work? You can probably speak to experience with proprietary software systems and record-keeping (which is a bigger deal than you’d think). Construction / landscaping / similar physical labor jobs? You know how to work hard in a range of weather conditions, keep a project on spec, have experience with complex project planning, and probably know a thing or two about basic safety stuff (don’t store heavy things above your head, lift with your legs, etc). You’re basically looking to communicate “I haven’t worked in this field, but here’s all the skills I have that will translate to this job.”
Realistically, if you’re coming in without a degree or a ton of animal experience, you’re much more likely to be able to get a job at smaller, non-AZA facilities to start (they might not even be zoos - there’s sanctuaries and petting zoos and all sorts of other professional animal care gigs). And this is fine and good! There’s lots of good ones out there. You can always use experience gained there to move up in the field, if it’s your dream to work at an AZA facility specifically. And a lot of people do that - you’ll hear some places talk about how they know they’re training zoos, because their staff get a foot in the door and then consistently leave for other facilities after a couple years. But there’s also a lot of reasons to stay with some of the smaller facilities. They’re often in areas with cheaper cost of living, and so a zookeeping salary will go farther. I’ve also seen that a lot of the smaller facilities - ones where like, staff know and interact with the zoo director frequently - tend to take better care of their staff. They may not be able to increase salary, but I’ve seen some of those facilities go the extra mile for their people in other ways when it’s possible. It’s a very different experience than being a small cog in the giant machines that are many AZA zoos. It’s the sort of thing you have to vet carefully, but when you find a small facility that really invests in it’s people, it can be very worthwhile.
You also have to think about the fact that you don’t have to start in zookeeping to get an animal care job! I’ve seen a lot of people start in education or in summer camp staff, and then use the relationship with the facility and their track record in those jobs to transition into animal care. Especially education, if you’ve got the skill-set, because you’re often working with ambassador animals or in collaboration with the teams that care for them. I’ve seen some people start in facilities or ground crew, too, but I think that’s less common. Getting your foot in the door somehow and building relationships is one of the biggest parts of getting a job in the field if you’re not following the traditional pipeline.
If you’re near enough to a smaller facility that you can visit regularly, do. Learn as much as you can about the zoo and what they do and what they’re involved in, to show that you’re interested and invested, and then go talk to someone there. Tell them exactly what you told me: this is a dream, and you’re really interested in their facility specifically, and you’re wondering what you should do to build a resume to apply for a job there. At worst, you’ll get some advice. At best, they might take a chance on you. I’ve heard of it happening. (The hardest part of this is, honestly, figuring out who to talk to - it’s not the sort of thing where you can just ask a keeper while they’re cleaning. But you can find opportunities, and then ask if there’s someone in management who might have time to answer a couple questions.)
So in short: yes. It’ll take some work and time, and probably some free labor, but it’s doable. More so now than any other time recently. Good luck!