Because of neighbors complaining about the window vent, I won’t be able to use my Glowforge this summer, since everyone has their ACs running and sucks up the fumes I vent 
And just after my neighbor complained, my air filter ship date changed from July to October!
Has anyone been able to make a cheap alternative? I’m in an apartment, so it has to be something small.
Search these forums, there have been others that have done some ‘home made’ stuff and one that I remember who bought a high-end professional filter (not cheap) but it apparently does work well.
Search amazon for “new neighbors”. They can be delivered in 2 days if you’re prime 
This doesn’t really help you, but if they smell your fumes, it won’t be limited to summer. Ac units don’t typically pull air from outside. They simply remove the heat from the air already in your house. Some types of units (think window mount) may give more ways for outside air to get in if not mounted properly, but if they are complaining, they probably will all the time.
Everyone in my area uses window mount. In the winter, everyone has their windows closed due to cold, so it hasn’t been an issue. I’ve had my glowforge since November.
You could start cooking with a lot of Onions and Garlic?
Instructables has some tips on making your own laser filters – look for the “fume coffin” for example.
Is moving to the top floor an option?
I suspect it’s more of an open window thing when it’s nice out as an AC unit cooling external air and exchanging it with indoor air would be odd, but the how doesn’t really matter.
Some units do air-exchange (with a cross current heat exchanger). Our house has a whole-house one for the HVAC which was put in by code. In fact I have to remember to shut down my exchanger when I am smoking meats as that plume is near the intake and the house rapidly will fill with smoke. I think someone should try a pre-exhaust filter just to reduce your plume from the GF prior to exhausting outside for reduction of neighbor annoyance rather than trying to do an indoor exhaust filter. Much safer if it doesn’t quite work to remove toxins, since you were exhausting them anyway.
My friend’s house has a similar setup, but these sound like Home Depot window units. It’s been a while since I owned one; I have a hard time believing it’s standard in a window unit.