You’d need to be able to lift about five pounds.
The problem isn’t the weight, it’s being able to balance it and perform repetitive/continuous motions over an extended period of time. This is where the “strength” and “size” misnomers come in for a lot of people.
The kind of physical activity required is like being able to do a bunch of pushups or run laps around a track. It’s not a strongman’s one time five hundred pound lift.
Your character can be any size, be any shape, and weigh anything.
The skills they need fall more in line with being able to swing the axe multiple times, balance for its weight, swing it fast enough to hit their target, and recover (get themselves into a ready position so they can strike again) quickly.
The recovery is the key bit because recovery is where the openings are and where most of the critical mistakes happen.
90% of the time, the moments when your character is going to get hit will happen in the moments preceding their strike (their windup) or in the moments after it doesn’t land/misses/connects poorly. “Recover” is one of the most difficult concepts for the inexperienced fighter to grasp and most of them don’t do it, they don’t reset their defenses to ready for the next strike or block an incoming attack. It is difficult to keep up a continuous assault if your unfamiliar with the concept or the weapon in hand.
For example: the trick with using a fire axe as a weapon is to swing it in a figure eight pattern, and keep it moving. This allows the weapon to move faster via its own weight and reduces the strain on the arms. Once it starts moving, you ensure that nothing can stop it except for an incoming body. The continuous motion also creates a solid, intimidating defense.
The fire axe is in a category similar to a machete. It’s the cousin of a real weapon and can act as a weapon when necessary much more easily than trying to transition a dinner plate into a weapon to beat people with. Hammers, sledge hammers, culinary knives, dinner knives, etc, are in that same category.
They aren’t “improvised” in the same way a beer bottle or a garbage can lid is, they’re much closer to being weapons and make the transition fairly easily. Call them second-cousins. They’re not as suited for the situation as the medieval weapons designed for war, but they’ll work in a pinch.
However, unless they have a background in HEMA, most people who pick up a fire axe are going to use it the way they think an axe should be used. They aren’t going to think about figure eight patterns, attacks on alternate angles, spinning defenses, and rolling strikes. They’re going to use it the traditional way, like a lumberjack or a fireman trying to break down a door or split some wood. (Which works perfectly well when dealing with stationary objects that can’t fight back.)
This is going to be where the problems of the axe occur. While the overhand is a very powerful strike, there’s a reason why it was generally performed in conjunction with a shield.
The overhand/overhead motion creates huge openings in the defense both coming and going, it’s also repetitive and easily adapted to. When you bring your arms up, you expose your entire torso. When the arms come down, your head is now in an easily reachable range. The time which it takes to lift the axe back into position and bring it down are where the openings are.
For most people, axe strikes are also stationary.
What the axe has in its favor is that it is a recognizable weapon and also terrifying. The axe has been the favored weapon of Hollywood horror monsters, it’s recognizable for what it can do, and person threatened with it will know that they are being threatened with a weapon.
This isn’t like a character standing around with a bottle of hairspray and a lighter while pointing it at their aggressor, a beer bottle, or just a can of spray paint.
Walking out with an axe is like walking out with a knife, or even a sword. It may seem weird for the situation, but their opponent is going to what it means, what it is, and what it can (potentially) do.
While the weapon can’t fight your battles for you, intimidation and headgames are part of warfare. If your character wants to intimidate an attacker or an enemy, then the fire axe is going to be a lot more useful than the frying pan or the dinner plate.
Can any character pick up a fire axe and go to town?
If you find yourself asking the question of “Can X do Y?” when it comes to combat. The answer is probably going to be yes, especially if it involves size, weight, height, or any of those statements about sex, gender, and body type.
Much as Hollywood and society at large want us to believe that the only ones capable of combat are six foot tall men between 180 to 225 pounds, life doesn’t work like that.
Physical activity is as much a matter of mind as it is body. You can learn to adjust to your body, condition your body, and adapt your body to the technique. It doesn’t matter who your are or your size, if you try you can learn to do the thing. If you decide to give up because of some arbitrary reason, then you won’t.
Most of us give up inside our own heads before we try.
And the only combat metric that matters is: did you live?
After that, everything is gravy.
When working with fiction, we create a simulacrum of real life. The point is to stick in enough “real life” bits to sell the audience on the suspension of disbelief.
What matters most is that you asked the question.