Can you even open the door of the cabinet and if so how wide if it's flush against the beam. What does the otherside of the window look like? How close to the window are the cabinets on the other side of the window. If there are any I would be tempted to balance them. I'm not even sure I'd put in a filler, but maybe.

You can open the door the full 90 degrees with it flush against the beam. The other side of the window is shown below - it is a 27" blind corner cabinet. The cabinets are equidistant with the glass cabinet being 3" away from the beam. I am contemplating getting a 27" cabinet to replace the 24" cabinet shown to keep the cabinet/window spacing symmetrical, but not having the 3" gap, but not sure if it is worth the hassle and extra price. I was just not a fan of the 3" gap, but not sure if having it flush against the beam looked right either!

As blfenton says, I'd make symmetrical with cabinets on other side of window, {equal distance from window casing) I'd also be inclined to no filler, and leave away from the beam, perhaps enough for a crown to return?

Filler.

Filler and hinge restrictor if you don't want shattered glass.

I have a header too exactly like yours. We chose to not put the cabinet flush against the header. We left about 5" between the header and the cabinet.

I'm not a hard-and-fast symmetry person but in this case it is something I would strongly consider by having the two cabinets set equal distance from the window casing, Then the decision is 24 or 27" cabinet with room for a filler. I do like to see balance achieved through visual weight and so in this case the 27" cabinet might be a better choice.
It really comes down to personal choice but the main thing to make sure of is protection of the cabinet and it sounds like filler and hinge restrictor is going to be needed.

Here is a kitchen that I did last Fall for a client. We kept the gap. The homeowner want to see the crown molding wrap all around 3 sides. Your kitchen is a little different, but thought you might like to see pictures of other jobs.

https://www.houzz.com/photos/showplace-wood-products-quarter-sawn-white-oak-dayton-oh-transitional-kitchen-phvw-vp~26739144

There are only two views.....here's the other one:

https://www.houzz.com/photos/showplace-wood-products-quarter-sawn-white-oak-dayton-oh-transitional-kitchen-phvw-vp~26739070

Here you go.

There is actually a corner filler on the other side, so I think I would put a filler on this side against the beam.

I would make sure that there is symmetry at the window for sure, but I am not sure that because there is a corner filler on one side, there has to be one on the other.

Also, if you use a filler, wouldn't you need a side panel for the cabinet also.

Yup, symmetrical around the window. And I would seriously consider getting the 27" cabinet. It's not such a huge kitchen that you can throw away 3 inches! If you stick with the 24", instead of filler that goes all the way around, why not use drywall and make the beam appear to take a turn? I don't think you need filler to go all the way down to the bottom of the cabinet.

And be sure to get 120 degree hinges for the left door. Ninety degrees just doesn't do it.

Ok - I had him put it back up with with 3" space. I think we might have to stick with this option since it seems we need some space between the cabinet and the beam, and to go with the 27" cabinet and have still space, the cabinets would no longer be symmetrical to the window.

I was looking at your other thread and yes it looks good. Visual weight is good as well. I think 27" would have been too big and not fit properly.

That looks wonderful!