I wasn't trying to be snarky. My brain disengaged when I was googling pictures to try to find an example. I know the vent needs to be on the trap arm before the drain goes down. I was trying to figure out the best way to do that. I'm trying to visualize the solution you are suggesting but I think I need to see a diagram.
The trap needs to tie in to the vent with a tee and then go down to the long sweep.
Something like this-- even if you need to get some bends in there to make it happen. I think the drain pipe will have to be lowered, unless you are able to raise the trap more.
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If the window was more than 6" above the flood level of the sink, you might be able to run the trap arm under the sill and tie in to that vent, but most of those windows are rarely high enough. This is why putting a huge window over a sink and not having it high enough to allow for the vent is a problem. But its's something I see all the time.
I'm no expert but I am wondering if a loop vent (aka island vent) would be ok. Some people might just slap in an AAV and be done with it, but it is best to avoid those when you can have an atmospheric vent.