There are some measures you can take that might help. Make a recording Booth by draping blankets over microphone stands (boom stands turned horizontal to make a 'T' work great for this but anything you can drape a blanket over will work). Two of these in a v shape can work well to cut unwanted room reflections as well as noise from the street. Use a close miking technique with low gain settings (this will help reduce picking up ambient noise). Heavy drapes or curtains over the window as opposed to just blinds can help reduce noise from the street. Or you can hang a blanket over it or put some foam in there too. Even pillows will help. Can even prop pillows in the window frame. Also blankets or pillows on any hard furniture or surfaces to absorb noise and reduce reflections (room reverberations) can help.
Because this will result in a very dead tone you will need to add reverb post recording. Remember that less is better and add just enough to add some ambience. I alsomprefer to record in mono when dealing with sub par recording space as it's easier to position one mic where it will pick up less noise. The reverb added will add a bit of spacial stereo to compensate. Good monitoring headphones are very helpful as they will allow you to hear what the mic hears and can make finding optimal placement with least ambient noise much easier. Otherwise it's pretty much trial and error. Don't skimp on these.
You might also find a time when there is less traffic and other ambient noise and take advantage of the room and do stereo micing and get natural ambience without having to add reverb.
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