Will not pass here because of 30" clearance requirement above the gas stove. You can not have a vinyl window above 12" above the stove.

Move the range.

I think you may want to move the window, if possible (can you match the siding material?). Having a window behind the range looks really nice but it is hard to clean, and will get dirty pretty quickly as steam condenses on the cold glass when you cook. If you moved the window to the left in your picture you could still see outside while at the stove and you would have an easier time with the vent hood decision.

If you do move the window, consider a casement (crank out) style that is made to look like a double hung to match your other windows. They are easier to operate when leaning across a counter.

All of the ranges in front of the windows pics posted above are done incorrectly, and unsafely. That ^ “Design” is too. That vinyl windows is going to melt,the wood sill is going to char, and the glass is going to get filthy or break into smithereens. It would need at least a 6” rear clearance, or a back guard, and an inoperable tempered glass window to safely work. It has none of that.

It’s a fire and a lawsuit waiting to happen.

PinnedYourRisk “E-designers” with or without mail order ”training”create all kinds of havoc when they step out of their pick-a-color and shop on Wayfair lanes into something where actual knowledge and real competency needs to be involved. Things like fire safety, building codes, materials tolerances all seem to take a back seat to “pretty”.

Hire a REAL Kitchen Designer and pay them to do this over. It’s your fail. Own it. Learn from it.

if you cannot move anything in the kitchen.....then the window could and should be changed.....you could get an aluminum FIXED window.....Operative windows near gas flames are to be avoided.....So leaving a window , but inoperative, easy to clean and safe framing , may be your best of poor and costly options. I don't know for sure, but glass block allows light, and is another NON working way of handling the existing opening. Have you sorted thru all options related to moving the range?

Ignoring all of the reasons why the window is a problem/safety hazard and dealing with the hood out of context, a commercial-like configuration hood with its guts above the ceiling and its entry aperture 12 inches down from the ceiling could work if all of its parts would fit. Stove overlap should be of the order of six-inches for that height. (The examples in the images above are too small for good capture and lack any capture volume.)

A similar volume above the ceiling would be needed, at a minimum, requiring a framed out area within the joists there.

For a 30-inch stove, a six-inch overlap would make the hood aperture 3.5 ft wide x 2.5 ft deep (to the wall) for an aperture area of 8.75 sq. ft. At 90 CFM/sq. ft., required maximum air flow rate should be around 800 CFM, which might be achieved with a 1200 CFM rated blower and a matching MUA system putting air into the kitchen across the room or directed across the room, or inserted into the house somewhere else.

This configuration basically requires an attic above the kitchen for ducting, or giving up some space (using a chase) in the room above. In commercial restaurant schemes, the blower and MUA system are usually on the roof, leaving only ducting to be dealt with. It would be possible with baffles at the ceiling height to have a cavity above the baffles with a side duct to the outside wall where the blower would be mounted. This wall should not be over a deck.

I guess the time to have figured this out would have been during the renovation stage. Right now there is no safe way to do this so change the window or change the placement of the stove.

Was there ever a range/cooktop in that place originally? It's so odd ... there also don't look to be any cabinets to the right of the range.

Post pics of the entire kitchen. I'm curious as to what the entire layout is. You're likely going to have to ditch the window because of safety reasons. What is supporting that countertop to the right of the range?

If there is a roof right above the ceiling, one might remove the window, use a normal wall mounted hood, and put in a skylight.

"...when they step out of their pick-a-color and shop on Wayfair lanes into something where actual knowledge and real competency needs to be involved."

Priceless.

Post the whole layout. Everything is fixable. We all had to start somewhere when it comes to Kitchen Design.

I’d suggest joining the NKBA and purchasing the NKBA Professional Resource Library to study up on Kitchen Design if you think you will tackle any future kitchen projects. There is a LOT to know, and unfortunately, Kitchen Design is barely covered in design school. You more or less have to work in a kitchen showroom and be mentored if you want to do kitchens. You pay for your mistakes there too, but there is a bigger network around you to help you. I’d be happy to help you fix this until you find a local mentor to work with.

https://store.nkba.org/collections/professional-resource-library