You could go to manual mode and overexpose the image. That would make the window all white (loss of highlight detail), but will bring out the cat a bit more. Example. If auto gives you 1/250s, try 1.5 f-stops longer, so 1/90s. The problem is that the window light may be so strong that there will be a halo around the cat and the fine hair detail will be lost.
Your camera may have something called +/- correction, or exposure correction, usually in the range of +/-2 f-stops. That way you could still use the camera in auto-exposure mode. If you have that, try going +1 or +2.
This is NOT the same as changing ISO on a digital camera; as pointed out by others, changing ISO will not address your problem. On old film cameras you can do exposure correction be changing ISO (because film sensitivity stays the same; disregarding pull/push processing), but that's a different story.
Flash will work no problems. Remember though, that then you need to be at an angle to the window to avoid reflection of the flash from the window back into the camera lens. The wider angle lens you use, the more you have to be at an angle (remember incident angle = reflected angle). So if you have a zoom lens, go as long as possible. There's a downside, as the further you go from the subject, the more powerfull flash you'll need. To counteract that effect, you could increase ISO, but you will get grainier images and more color noise [no free lunch, sorry]. Build-in flashes are usually pretty wimpy.
Reflector will help. Difficult to predict what the result will be, depends on the size of the window/light source, position of the reflector, reflector material (foam board reflects less light than tin-foil/lite disc). Reflectors will most likely give the best results.
Also remember, you can combine various approaches, e.g., reflector with exposure correction. First sounds quite complicated, after a while it's second nature.
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