The only thing needed for a roof mounted fan with a vent hood is a roof. And a duct through the roof. Not a big deal at all. Neither is going up and sideways, to outside the home, concealed in a false beam or inside of , or on top of, cabinets, if needed. ETC. There are TONS of ways of accomplishing ventilation that all involve someone knowledgeable ON SITE inspecting what you have.

Or you could post pictures and a diagram of the kitchen and get more ideas.

I have a Jenn Air downdraft that is ok. If you have a gas cooktop, it is not good, because it pulls the flame. If you have induction or electric, then it may be fine. Not as good as a hood. But you’d have to vent it through the floor joists. If you can find a way to do a vent hood I would recommend that instead.

An attic provides space to (a) install a silencer which will lower noise levels if the blower is on the roof or in-line closer to the roof than the silencer, and (b) room to maneuver the duct path so the roof blower is positioned in an optimal position. These advantages are not essential.

Generally, the best capture of cooking plumes in residential settings occurs with overhead canopy type hoods. There are recirculating overhead hoods that are better than no hood, but venting to the outside is better.

Down-draft apertures, or pop-up panels that move cooking effluent downward, have limited capture of upward rising plumes, and require space under the floor to duct the captured plume components outside.

You don't need an attic for a vent hood, but if you have a second story, that makes it trickier (with or without an attic). If no second story, easy peasy. I imagine you have a flat roof in this scenario? The hood vent costs should not be large as long as you don't need makeup air. (In our old California bungalow that isn't remotely air tight, no problem.) We did the kitchen hood in our house years ago but opened that section of the wall ourselves, ran the vent, hired an electrician to wire it and a drywall guy to close the wall, hung the hood ourselves, and hired a roofer to put on the cap. The whole thing was well under $1K plus the cost of the hood. While costs have gone up since then, we had a roof vent for a bathroom in the Bay Area put in a couple of months ago for a few hundred dollars, so it shouldn't be exorbitant. Well worth the cost if you're doing other kitchen upgrades.

Look on the bright side. You'll have an induction cooktop or range with massively improved performance over older electric. You could use it more. Get good venting.

Downdrafts suck

Downdrafts actually suck less

Does the kitchen have an exterior wall? If so, you could move the cooker and vent thru the wall. There are many range hoods that give you the option to vent either up thru the roof or out the back and thru the wall.