Can I get a zoom shot like this on a low budget?

Basically for a film project I want to do, I want a zoom shot like this, like the one you see at 1:38 into the clip:

https://www.youtube.com/watch?v=_ysVoV3x5Zo

Basically it starts out as a medium close up of the woman, then it zooms far back, putting her in the background. Basically I want a shot like that.

However, it's very difficult on a microbudget to a lens that can do that. Even the rental store, has all kinds of video equipment, but not those kinds of zoom lens. So I tried my lens as a test, which is a variable aperture lens. The aperture changes as you zoom back and forth. I asked for advice on that, and people were telling me that the lens was changing apertures as I zoomed back and forth. So I made sure and did in a test, here:

https://youtu.be/ztSnRwE8j4A

Now I did that test with the aperture at f8. I looked to make sure, and it stayed at f8, the entire time. I also tried more zooms back and forth that I didn't post, but it was f8, the entire time.

So it possible to get the kind of shot that you see in The Wild Bunch without that specific of a zoom lens that can be a constant aperture? One option is put the camera on a steadicam, and run with it. But I cannot run as fast as the zoom you see in that shot. It zooms back about 40 feet in less than a second, and I cannot run that fast with the steadicam. A dolly would probably be even slower.

Does anyone have any suggestions?

I thought about maybe getting a 4K camera and then zooming into the footage in post, and then zooming back in post, cause then I would still have 1080p in the end. Is that a good option?