Can someone be photographed outside after sunset without using flash?

A streetlight in the park is sufficient for a photograph with modern cameras. However, the photographer doesn't need to be under the streetlight — the subject does. The photographer can (and, given the situation, sounds like should) stay completely in the dark.

Although it's slightly technical, take a look at this chart of exposure values at Wikipeda. In part:

Night street scenes and window displays        7–8
Night vehicle traffic                            5

If your city park is well-lit by streetlights, it falls in this range. Let's assume the darker end of the range. This would mean that with an f/2.8 lens and ISO 3200, you would be able to take a photo with a shutter speed of ¹⁄₁₂₅th of a second — fast enough that subject motion blur won't be a big problem.

Any DSLR with a decent lens will be able to do that. The kit lens and cheap zooms won't have as fast an aperture, but if new enough the camera will have higher ISO to compensate. A really cheap point and shoot might struggle, but a decent one will be well within this.

If your character is a photographer with pro-level gear, this isn't even a problem. If you can give your photographer a really big telephoto lens, that should look impressive enough that you shouldn't need to explain that it would work for the pedants in the audience.