You are looking for a flavor of "unicorn". An affordable, durable, low-hand means of printing low-volume, full-color art on dark garments.
While the ideal of the unicorn is unattainable (at least so far), there are various ways to cobble together an old nag with a toilet paper core stuck to its forehead. What you suggest is in theory one of them. Sublimation works with plastic, polyester in particular. Screen printing inks, as far as I know, are not made out of polyester. Though somewhere along the way I have seen a video where a guy screen printed some goop on a shirt then seemed to do a (maybe) sublimation transfer over that ... was a while ago, and he was being vague.
Anyway, sure, can be done one way or another. But after you have succeeded in getting a thick opaque rectangle of white polyester goop down on your black shirt and have sublimated an image to it, is it a unicorn or an old nag with a paper cone? You might have succeeded in creating a colorful version of a bullet proof vest, or maybe no worse than a decently printed full-chest Plastisol print, but certainly not a zero-hand sublimation print. Is the polyester-laced goo as durable as Plastisol? Hell, maybe it would even work on regular Plastisol to some extent, don't know. I'm sure someone will chime in with an experiment they have done, or seen done. I don't know what the guy used that I described above, as he was being cagey about the process, but still feeling the need to show off.
I've been messing about with my own cone-headed nag. Discharge print a white rectangle and then heat press a JPSS transfer over it. Of course, got to wash that nasty discharge stuff out first, and need to allow a bit of slop so the transfer overlaps onto the colored part of the garment. Again, the end result is not a zero hand print, but a JPSS transfer, which especially at first feels like what it is, a piece of plastic stuck to the shirt (the feel improves with a few washings, but is still not zero hand).
In my case, my cone-headed nag is good enough for my purposes. I discharge print garments with white rectangles in bulk, then print and press the transfers as needed for orders. So a half-butted way to POD full-color art on dark garments. Oh, and I'm printing the JPSS with sublimation ink, though it is intended for use with pigment inks. I'm not doing that because of the miracle of sublimation, but because due to the covid supply chain catastrophe, I had to convert my 13x19 printer to sublimation, so no longer have a pigment printer large enough to do shirt transfers. I've been told that using sublimation inks with these transfers is inadvisable, but it seems to be working out okay so far.
But, again, no particular reason to use sublimation unless it is the only printer you have access to, since one is negating all the special attributes of sublimation (zero hand, extreme durability) by taping a paper cone to a nag in the first place. That nice, nice sublimation ink will only be as "magical" as whatever trick you use to get it to show up on a black shirt, and only that durable, and only that nice feeling.
So what is your specific use case?
EDIT Ha! I remembered that we have these fancy new emoticons ... 🦄